Method for correcting three-dimensional measurements of a spherically mounted retroreflector

ABSTRACT

A method of measuring spherically mounted retroreflector (SMR) with a 3D coordinate measurement device such as a laser tracker. The SMR includes an open-air cube corner retroreflector having a vertex point located near a sphere center of the SMR. Measurements of the SMR to the vertex point are moved to the SMR sphere center by accounting for SMR depth error and SMR runout error.

FIELD OF INVENTION

The present invention relates in general to methods for measuringspherically mounted retroreflectors (SMRs) and in particular to methodsfor determining surface coordinates and three-dimensional distancesbased on measurements of SMRs.

BACKGROUND

There is a class of instruments that measures the coordinates of a pointby sending a laser beam to a retroreflector target in contact with thepoint. The instrument determines the coordinates of the point bymeasuring the distance and the two angles to the target. The distance ismeasured with a distance-measuring device such as an ADM or aninterferometer. The angles are measured with an angle-measuring devicesuch as an angular encoder. A gimbaled beam-steering mechanism withinthe instrument directs the laser beam to the point of interest.

The laser tracker is a particular type of coordinate-measuring devicethat tracks the retroreflector target with one or more laser beams itemits. There is another category of instruments known as total stationsor tachymeters that may measure a retroreflector or a point on adiffusely scattering surface. Laser trackers, which typically haveaccuracies on the order of a thousand of an inch and as good as one ortwo micrometers under certain circumstances, are usually much moreaccurate than total stations. The broad definition of laser tracker,which includes total stations, is used throughout this application.

Ordinarily the laser tracker sends a laser beam to a retroreflectortarget. A common type of retroreflector target is the SMR. In mostcases, the term SMR is applied to a cube-corner retroreflector embeddedwithin a metal sphere. However, the term SMR may also be applied to acateye retroreflector embedded with a metal exterior spherical portion.Such a cateye retroreflector may be constructed in a shape of a sphereor in the shape of two adjoining hemispheres. A cube-cornerretroreflector includes three mutually perpendicular reflectors. Thevertex, which is the common point of intersection of the threereflectors, is located near the center of the sphere. In its normaltracking mode, the laser tracker sends a beam of light from the trackerto a position near the vertex of the SMR. As long as the beam of lightstrikes the vertex, the beam of returning beam of light retraces thepath of the outgoing beam of light back to the tracker. If the beam oflight strikes the SMR slightly off the vertex, the beam of light willreturn parallel to, but not exactly coincident with, the outgoing beamof light. A servo system within the tracker adjusts the direction of thebeam emitted by the tracker to bring it back to the center, therebyallowing the beam to follow a moving retroreflector. Because the vertexis nearly coincident with the sphere center of the SMR, theperpendicular distance from the vertex to any surface on which the SMRrests remains nearly constant, even as the SMR is rotated. Consequently,the laser tracker can measure the 3D coordinates of a surface to arelatively high accuracy by following the position of an SMR as it ismoved over the surface. Stating this another way, the laser trackerneeds to measure only three degrees of freedom (one radial distance andtwo angles) to characterize the 3D coordinates of a surface.

An SMR may also be used to measure the distance between two nests. Aparticularly useful kind of nest is a kinematic nest, which has theproperty that an SMR can be repeatably positioned in the nest. One typeof nest makes contact with the SMR surface at three points. Some typesof nests are magnetic nests that hold the SMR securely in place againstthe nest contact points.

Some laser trackers have the ability to measure six degrees of freedom(DOF), which may include three translations, such as x, y, and z, andthree rotations, such as pitch, roll, and yaw. An exemplary six-DOFlaser tracker system is described in U.S. Pat. No. 7,800,758 ('758) toBridges, et al., incorporated by reference herein. The '758 patentdiscloses a probe that holds a cube corner retroreflector, onto whichmarks have been placed. The cube corner retroreflector is illuminated bya laser beam from the laser tracker, and the marks on the cube cornerretroreflector are captured by an orientation camera within the lasertracker. The three orientational degrees of freedom, for example, thepitch, roll, and yaw angles, are calculated based on the image obtainedby the orientation camera. The laser tracker measures a distance and twoangles to the vertex of the cube-corner retroreflector. When thedistance and two angles, which give three translational degrees offreedom of the vertex, are combined with the three orientational degreesof freedom obtained from the orientation camera image, the position of aprobe tip, arranged at a prescribed position relative to the vertex ofthe cube corner retroreflector, can be found. Such a probe tip may beused, for example, to measure the coordinates of a “hidden” feature thatis out of the line of sight of the laser beam from the laser tracker.

As explained hereinabove, the vertex of a cube corner retroreflectorwithin an SMR is ideally placed at the exact center of the sphere intowhich the cube corner is embedded. In practice, the position of thevertex is off the center of the sphere by up to a few thousandths of aninch. In some cases, the difference in the positions of the vertex andthe sphere center are known to high accuracy, but this data is not usedto correct the tracker readings. In the accurate measurements made withlaser trackers, this error in the centering of the cube cornerretroreflector in the sphere is sometimes larger than the errors fromthe distance and angle meters within the laser tracker. Consequently,there is a need for a method to correct this centering error.

Most of the SMRs in use today contain open-air cube cornerretroreflectors. There are some SMRs that use glass cube cornerretroreflectors, but in most cases these have limited accuracy. Becauseof the bending of the light entering such glass cube corners, the lightappears to travel in a direction that is not the true direction withinthe cube corner. Consequently, SMRs made with glass cube corners tend tobe made very small, as this reduces error, and they tend to be used inapplications where the highest accuracy is not required. A method forminimizing this error using a six-DOF laser tracker is given in U.S.Pat. No. 8,467,072, the contents of which are incorporated by reference.

In many cases, the SMR of interest is an open-air cube corner ratherthan a glass cube corner, and the laser tracker measures only threedegrees of freedom rather than six. Measurement error associated withsuch an SMR and tracker combination result both from errors in vertexcentering and in sphere diameter. These errors can be corrected to anextent by purchasing a more expensive SMR having smaller centering andradius errors, but the errors cannot be eliminated. Furthermore,expensive SMRs are cost prohibitive in many applications. There is aneed for a method to correct these errors, even for relativelyinexpensive SMRs.

SUMMARY

According to one aspect of the invention, a method is provided formeasuring a spherically mounted retroreflector (SMR) with a device, themethod comprising the steps of providing a first SMR, the first SMRincluding a first body and a first retroreflector, the first SMRincluding a first reference point, the first body having a firstspherical exterior portion that has a first sphere center and a firstsphere radius, the first body containing a first cavity, the firstcavity sized to hold the first retroreflector, the first cavity open toa region outside the first body, the first retroreflector at leastpartially disposed in the first cavity, the first retroreflector beingan open-air cube-corner retroreflector, the first retroreflector havinga first set of three mutually perpendicular planar reflectors thatintersect in a first set of three lines and in a common first vertexpoint, the first cavity including an air-filled region interior toreflecting surfaces of the first set of three planar reflectors, thefirst retroreflector having a first axis of symmetry relative to thefirst set of three lines, the first SMR having a first SMR runout planeperpendicular to the first axis of symmetry and passing through thefirst sphere center, the first SMR having a first SMR intersectionpoint, the first SMR intersection point being a point of intersection ofthe first axis of symmetry with the first SMR runout plane, the firstSMR having a first error vector extending from the first vertex point tothe first sphere center, the first SMR error vector having a first SMRdepth error vector component and a first SMR runout error vectorcomponent, the first SMR depth error vector component being a vectorthat extends from the first vertex point to the first SMR intersectionpoint, the first SMR runout error vector component being a vector thatextends from the first SMR intersection point to the first spherecenter, the first SMR depth error vector component having a magnitudeequal to a first SMR depth error; providing the device, wherein thedevice has a device frame of reference fixed with respect to a base ofthe device and a light source that emits a first beam of light, thedevice being configured to measure a target distance and two targetangles from the device to the first vertex point, the two target anglesgiven with respect to the base; providing a processor and a memory;providing computer readable media having computer readable instructionswhich when executed by the processor calculates first three-dimensional(3D) coordinates of the first sphere center in the device frame ofreference; determining the first SMR depth error and the first SMRrunout error vector component; storing as first stored values the firstSMR depth error and a numerical representation of the first SMR runouterror vector component; reading by the processor the first storedvalues; and performing a first measurement, the first measurementincluding steps A through J: A) providing a rule for orienting the firstSMR to obtain a first preferred orientation of the first SMR; B)determining, by the operator, the first preferred orientation of thefirst SMR based at least in part on the rule; C) orienting, by theoperator, the first SMR in the first preferred orientation, the firstpreferred orientation based at least in part on the first referencepoint and on the axis of symmetry; D) determining by the processor thefirst preferred orientation in the device frame of reference based atleast in part on the rule; E) sending the first beam of light from thelight source to the first vertex point in a first beam direction and inresponse receiving at the device a first reflected light; F) measuring,from the device to the first vertex point, a first target distance and afirst set of the two target angles based at least in part on the firstreflected light, the first target distance further based at least inpart on a speed of light over a path traveled by the first beam oflight; G) determining the first beam direction in the device frame ofreference based at least in part on the first set of the two targetangles; H) determining with the processor 3D coordinates of the firstvertex point in the device frame of reference based at least in part onthe first target distance and the first set of the two target angles; I)executing by the processor the computer readable instructions, thecomputer readable instructions performing a mathematical transformationof the 3D coordinates of the first vertex point to obtain the 3Dcoordinates of the first sphere center in the device frame of reference,the mathematical transformation including translating the 3D coordinatesof the first vertex point along the first beam direction by the firstSMR depth error and along a direction perpendicular to the first beamdirection, the translating along the direction perpendicular to thefirst beam direction being based at least in part on the first beamdirection, the numerical representation of the first SMR runout errorvector component, and the first preferred orientation of the first SMR;and J) storing the 3D coordinates of the first sphere center.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, withreference to the accompanying drawings which are meant to be exemplary,not limiting, and wherein like elements are numbered alike in severalfigures, in which:

FIG. 1 is a perspective view of a laser tracker and an SMR according toan embodiment;

FIG. 2 is an illustration of a laser tracker, an auxiliary unit, and anexternal computer according to an embodiment;

FIG. 3 is a block diagram showing elements in the payload of a lasertracker according to an embodiment;

FIG. 4 is a perspective view of elements used in replicating a cubecorner retroreflector;

FIGS. 5A-C are perspective, cross-sectional, and front views,respectively, of an SMR that includes an open-air cube-corner slugembedded within a sphere according to embodiments;

FIGS. 6A-C are perspective views of the SMRs to which have been added areflective region, a barcode pattern or serial number, and an RFidentification tag, respectively, according to embodiments;

FIGS. 7A-B are front and side sectional views, respectively, of an SMRhaving a cube corner retroreflector not perfectly centered within asphere;

FIG. 8A is a perspective view of a portion of a cube cornerretroreflector with its axis of symmetry, and FIG. 8B is magnified viewof the SMR vertex point and sphere center with error vector and errorvector components according to an embodiment;

FIG. 9A is a perspective view of a portion of a cube cornerretroreflector including a reference mark and an SMR runout referenceplane, and FIG. 9B is a magnified view of the SMR vertex point andsphere center showing the SMR runout reference ray and the SMR runoutreference angle according to an embodiment;

FIG. 9C is a perspective view of a portion of a cube cornerretroreflector including a reference mark and a beam runout referenceplane, and FIG. 9D is a magnified view of the SMR vertex point andsphere center showing the beam runout reference ray and the beam runoutreference angle according to an embodiment;

FIGS. 10A, 10C are perspective and front views, respectively, of an SMRthat provides a connector socket, and FIG. 10B is a cross-sectional viewof an SMR showing a temperature sensor configured for electricalconnection to connector cable, also shown, according to an embodiment;

FIG. 10D shows the elements of FIG. 10C with the addition ofself-contained temperature measurement and communication unit, FIG. 10Eis a schematic view of electrical components within the temperaturemeasurement and communication unit, and FIG. 10F is a pictorialrepresentation of a hand holding an SMR, wherein a temperaturemeasurement and communication unit is attached to the hand;

FIG. 11 is an SMR to which is attached an interface unit that includes abattery and antenna for use with a temperature sensor;

FIGS. 12A-E are schematic illustrations of the errors resulting from themisalignment of the axis of symmetry of an SMR with the beam of lightfrom a 3D measurement device;

FIGS. 13A-13F are perspective and schematic representations ofalternative methods for aligning an axis of symmetry of an SMR with abeam of light from a 3D measurement device according to an embodiment;

FIG. 14A shows a kinematic nest and support axis, and FIG. 14B shows akinematic nest receiving an SMR;

FIG. 15 shows a mathematical model of the kinematic nest of 14A;

FIGS. 16A, 16B show front and side views of SMRs held by kinematicnests, respectively, and FIG. 16C shows that errors in the SMR radius donot significantly affect a measured length;

FIG. 17A shows side views of SMRs held by kinematic nests with one ofthe nests perpendicular to a desired measurement direction, and FIG. 17Bshows that errors may be significant for this case;

FIG. 18 illustrates a method of obtaining accurate 3D measurements of anSMR sphere center for a device located at two stations while performingan SMR alignment at a single station;

FIGS. 19A, 19B illustrate that the direction of the maximum runout errorvector component, which may in an embodiment be aligned to a referencepoint on the SMR, may have a significant effect on measurement error;

FIGS. 19C, 19D illustrate a general approach to aligning a runout errorvector component to minimize measurement error;

FIGS. 20A, 20B show a distance measurement made to an SMR in frontsightand backsight modes, respectively, and FIG. 20C shows a distancemeasurement made to a home position;

FIG. 21A shows a method for measuring a distance between two sphericallymounted retroreflectors, FIG. 21B shows a method for determining findingan offset error in measured distance, and FIG. 21C shows a method forfinding the axis offset value for a coordinate measurement device;

FIG. 22 shows a method for setting a distance to the vertex of an SMR ina home position; and

FIG. 23 shows electronics and processors within a laser trackeraccording to an embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

An exemplary laser tracker 10 is illustrated in FIG. 1. An exemplarygimbaled beam-steering mechanism 12 of laser tracker 10 includes zenithcarriage 14 mounted on azimuth base 16 and rotated about azimuth axis20. Payload 15 is mounted on zenith carriage 14 and rotated about zenithaxis 18. Zenith mechanical rotation axis (not shown) and azimuthmechanical rotation axis (not shown) intersect orthogonally, internallyto tracker 10, at gimbal point 22, which is typically the origin fordistance measurements. Laser beam 46 virtually passes through gimbalpoint 22 and is pointed orthogonal to zenith axis 18. In other words,laser beam 46 is in a plane normal to zenith axis 18. Laser beam 46 ispointed in the desired direction by motors within the tracker (notshown) that rotate payload 15 about zenith axis 18 and azimuth axis 20.Zenith and azimuth angular encoders, internal to the tracker (notshown), are attached to zenith mechanical axis (not shown) and azimuthmechanical axis (not shown) and indicate, to relatively high accuracy,the angles of rotation. Laser beam 46 travels to external retroreflector26 such as the SMR described above. By measuring the radial distancebetween gimbal point 22 and retroreflector 26 and the rotation anglesabout the zenith and azimuth axes 18, 20, the position of retroreflector26 is found within the spherical coordinate system of the tracker.

The device frame of reference 30 of the laser tracker 10 is fixed withrespect to the azimuth base 16, which is typically stationary withrespect to the tracker's surroundings. The device frame of reference 30may be represented in a variety of coordinate systems. It may berepresented in a Cartesian coordinate system having three perpendicularaxes x′, y′, and z′. It may be represented in a spherical coordinatesystem, a point 74 being represented by a radial distance 73 (r), afirst (zenith) angle 72 (θ), and a second (azimuth) angle 71 (φ). Theangle θ is obtained by using the projection of the point 74 onto the zaxis. The angle φ is obtained by using the projection of the point 74onto the x′-y′ plane. The laser tracker 10 inherently measures in aspherical coordinate system using one distance meter to measure r andtwo angular encoders to measure θ and φ. However, a point measured inspherical coordinates may be easily converted to Cartesian coordinates.In an embodiment, the gimbal point 22 is selected as the origin. Othercoordinate systems are possible and may be used.

The laser tracker 10 also includes rotating frames of reference. One ofthe rotating frames of reference is the payload frame of reference 35that aims the beam of light 46 toward the SMR 26. The payload frame ofreference rotates about the axis 20 and the axis 18. It should beunderstood that the term payload frame of reference may refer to thefinal beam delivery portion of any type of beam delivery system, notjust the payload 15 of FIG. 1. For example, the payload 15 may bereplaced by a minor that reflects the beam of light 46 toward the SMR26. The payload frame of reference 35 may be represented in a Cartesiancoordinate system having three perpendicular axes x″, y″, and z″ asshown in FIG. 1. In an exemplary payload frame of reference, the x″ axispoints in the direction of the outgoing laser beam 46, the y″ axispoints in the direction of the zenith axis 18, and the z″ axis points ina direction perpendicular to the x″ and y″ axes. The y″-z″ plane isperpendicular to the direction x″ of the laser beam. In an embodiment,the gimbal point 22 is the origin of the payload frame of reference 35.

The SMR 26 has an SMR frame of reference 40. The SMR frame of referencemay be represented, for example, in a Cartesian coordinate system havingthree perpendicular axes x, y, and z. The x, y, and z axes of the SMRframe of reference 40 move with the SMR 26 and are not in generalparallel to the corresponding axes x″, y″, and z″ of the payload frameof reference 35. In an embodiment, a vertex of a cube cornerretroreflector within the SMR is the origin of the SMR frame ofreference. The SMR 26 may be placed in contact with the workpiecesurface 61 at a point 63. To find the three-dimensional (3D) coordinatesof the point 63, the tracker first determines the 3D coordinates of thevertex of the SMR 26 using the distance and two angles it has measured.It then shifts the 3D coordinates of the SMR vertex toward the surfaceby an amount equal to the sphere radius of the SMR. The SMR 26 may alsobe used to measure 3D coordinates when placed on a kinematic nest, asfurther explained hereinbelow.

Laser beam 46 may include one or more laser wavelengths, or the beam 46may be a beam of light other than laser light. For the sake of clarityand simplicity, a steering mechanism of the sort shown in FIG. 1 isassumed in the following discussion. However, other types of steeringmechanisms are possible. For example, it would be possible to reflect alaser beam off a minor rotated about the azimuth and zenith axes. Thetechniques described here are applicable, regardless of the type ofsteering mechanism.

In exemplary laser tracker 10, locator cameras 52, 56 and light sources54 are located on payload 15. Light sources 54 illuminate one or moreretroreflector targets 26. In an embodiment, light sources 54 are LEDselectrically driven to repetitively emit pulsed light. Each locatorcamera 52 and 56 includes a photosensitive array and a lens placed infront of the photosensitive array. The photosensitive array may be aCMOS or CCD array, for example. In an embodiment, the lens of locatorcamera 52 has a relatively wide field of view, for example, 30 or 40degrees. In contrast, the lens of locator camera 56 may have arelatively narrow field of view, for example, to enable clear reading ofa bar code or a serial number of an SMR 26 held in a home nest 17, asdiscussed further hereinbelow. The purpose of the lens in a camera 52,56 is to form an image on the photosensitive array of objects within thefield of view of the lens. The image on the photosensitive array is sentto electronics, which may be internal or external to the photosensitivearray, to provide an electrical signal to a processor. The electricalsignal is evaluated by the processor to extract relevant informationsuch as images, text, array locations, and so forth. Usually at leastone light source 54 is placed near a locator camera 52 so that lightfrom light source 54 is reflected off each retroreflector target 26 ontothe locator camera 52. In this way, retroreflector images are readilydistinguished from the background on the photosensitive array as theirimage spots are brighter than background objects and are pulsed. In anembodiment, there are two locator cameras 52 and two light sources 54placed about the line of laser beam 46. By using two locator cameras 52in this way, the principle of triangulation can be used to find thethree dimensional coordinates of any SMR within the field of view of thelocator camera. In addition, the three dimensional coordinates of an SMRcan be monitored as the SMR is moved from point to point.

For a locator camera 56 designed to read bar codes, a light source isnot placed close to the camera as the bright flash of retroreflectedlight would prevent the camera from reading the much dimmer lines of abar code. Instead, the lights 54, which are too far away from thelocator camera 56 to retro-reflect the light from the retroreflectortarget 26 into the locator camera 56, may be used to illuminate the barcodes, if needed.

As shown in FIG. 2, auxiliary unit 70 may be a part of laser tracker 10.The purpose of auxiliary unit 70 is to supply electrical power to thelaser tracker body and in some cases to also supply computing andclocking capability to the system. It is possible to eliminate auxiliaryunit 70 altogether by moving the functionality of auxiliary unit 70 intothe tracker body. In most cases, auxiliary unit 70 is attached togeneral purpose computer 80. Application software loaded onto generalpurpose computer 80 may provide application capabilities such as reverseengineering. It is also possible to eliminate general purpose computer80 by building its computing capability directly into laser tracker 10.In this case, a user interface, possibly providing keyboard and mousefunctionality may be built into laser tracker 10. The connection betweenauxiliary unit 70 and computer 80 may be wireless or through a cable ofelectrical wires. Computer 80 may be connected to a network, andauxiliary unit 70 may also be connected to a network. Pluralinstruments, for example, multiple measurement instruments or actuators,may be connected together, either through computer 80 or auxiliary unit70. In an embodiment, auxiliary unit 70 is omitted and connections aremade directly between laser tracker 10 and computer 80.

The laser tracker 10 measures a distance r using either aninterferometer or an ADM. It measures an azimuth angle φ and a zenithangle θ using angular encoders. Hence the laser tracker measures in aspherical coordinate system, although the coordinate values for anymeasured point may be converted into coordinates in any other desiredcoordinate system, for example, the Cartesian coordinate system 30 ofFIG. 1.

It should be similarly understood that three degrees of translationalfreedom means three independent degrees of translational freedom.Another way of saying this is that the three directions corresponding tothe three degrees of translational freedom form a basis set inthree-dimensional space. In other words, each of the three directionscorresponding to a degree of translational freedom has a componentorthogonal to each of the other two directions.

FIG. 3 shows an embodiment for electro-optical assembly 400 of the lasertracker 10. Source elements 405 and 410 represent light sources andpossibly additional electrical and optical components. For example,source element 410 may represent a red helium-neon laser in combinationwith an interferometer. Source element 405 may represent an infraredlaser in combination with an ADM. Alternatively, the system may haveonly an interferometer or only an ADM. One of the source elements 405 or410 may have only a source of light without a distance meter. There maybe additional light sources (not shown) besides those contained withinsource elements 405 and 410. The source elements 405 and 410 may belocated in payload 15 or they may be located in one of the other partsof the tracker such as the zenith carriage 14 or azimuth base 16. Thelight source may be located in one section, for example, the azimuthbase, and the distance meter located in another section such as thepayload 15. The light may be routed from one location to another byoptical fibers, as explained in the '758 patent. Alternatively, thelight from the source may be reflected off a mirror that is steeredabout the zenith axis, and the distance meters kept in the azimuth base16. The light sources may include lasers, superluminescent diodes, lightemitting diodes, or others.

Light from source element 410 passes through beam splitter 420. Lightfrom source element 405 reflects off mirror 415 and beam splitter 420.If source elements 405, 410 contain light of different wavelengths, beamsplitter 420 may advantageously be a dichroic beam splitter thattransmits the wavelength of light emitted by source element 410 andreflects the wavelength of light emitted by source element 405.

Most of the light from beam splitter 420 passes through beam splitter425. A small amount of light is reflected off beam splitter 425 and islost. The light passes through beam expander 435, which expands the sizeof the beam on the way out of the tracker. Expanding the beam of lightis helpful because it enables the light to propagate a longer distancewith less change in beam size. The laser light 440 leaving the tracker10 travels to a retroreflector target 26. A portion of this laser lightreflects off the retroreflector 26 and returns to the tracker. The beamexpander 435 reduces the size of the beam on the way back into thetracker.

Part of the returning light travels to beam splitter 425. Most of thelight passes on to elements 405, 410 but a small amount is split off andstrikes position detector 450. In some cases, the light may pass througha lens after reflecting off beam splitter 425 but before strikingposition detector 450. The position detector 450 may be of severaltypes—for example, a position sensitive detector or photosensitivearray. A position sensitive detector might be a lateral effect detectoror a quadrant detector, for example. A photosensitive array might be aCMOS or CCD array, for example. Position detectors are responsive to theposition of the returning light beam. The motors attached to the azimuthmechanical axes and the zenith mechanical axes are adjusted by a controlsystem within the tracker 10 to keep the returning light beam centered,as nearly as possible, on the position detector 450.

The SMR 26 includes a body having a spherical exterior portion and aretroreflector. The spherical exterior portion contains a cavity sizedto hold a cube corner retroreflector, which is at least partiallydisposed in the cavity. The spherical exterior portion has a sphericalcenter. A cube corner retroreflector may be an open-air cube corner or aglass cube corner. An open-air cube corner retroreflector has aninterior portion of air, while a glass cube corner retroreflector has aninterior portion of glass.

A cube corner retroreflector includes three planar reflectors that aremutually perpendicular. The three planar reflectors intersect at acommon vertex, which in the ideal case is a point. Each of the planarreflectors has two intersection junctions, each intersection junction ofwhich is shared with an adjacent planar reflector for a total of threeintersection junctions within the cube corner retroreflector. The cubecorner retroreflector has an interior portion that is a region of spacesurrounded on three sides by the planar reflectors. In the case of anopen-air cube corner retroreflector, which is the subject of the presentapplication, the cavity includes an air-filled portion interior to thethree planar reflectors, the three intersection junctions, and thevertex. The cavity is open to an exterior of the body, which provides ameans for light to be sent into and reflected from the retroreflector.

There are at least three common methods for making open-air cube cornerretroreflectors: a replication process, a mirror insertion process, andan ECM process. FIG. 4 illustrates the replication process. A masterelement 510 is carefully machined to produce the characteristics desiredin the final replicated retroreflector. For example, the master element510 may be machined to make each of the three planar reflector faces 512almost exactly perpendicular to its two neighbors 512. The three planarreflector faces 512 of the master element 510 may be perpendicular toeach of the neighboring reflectors to within one or two arc seconds. Themaster element 510 is coated with a reflective material such as gold. Acube corner slug 520 includes a machined blank 522 coated with a thinadhesive layer of material such as epoxy. The cube corner slug 520 isbrought in contact with the master element 510. In doing so, the epoxylayer is brought into conformance with the shape of the master element510. After the epoxy cures and the slug 520 is lifted off the masterelement 510, the gold layer sticks to the epoxy, thereby providing thecube corner slug 520 with a reflective coating.

The second common method of making open-air cube corner retroreflectorsis the minor insertion process in which minor panels joined into acube-corner assembly are inserted into a cavity in the sphericalexterior portion. Three minor panels are joined together to be mutuallyperpendicular.

The third common method of making open-air cube corner retroreflectorsis the electrochemical machining (ECM) process. In some cases, theretroreflector and the spherical exterior portion are integrated into asingle unit. Such an SMR may be created, for example, by removing thecavity using a combination of traditional machining and ECM. Such an ECMprocess may be used to create three mutually perpendicular surfaces thatare flat and smooth. Such surfaces may be covered with a reflectivecoating such as gold or silver to provide the three reflective surfaces.

An SMR having an open-air cube corner retroreflector is illustrated inFIGS. 5A-C. FIG. 5A shows an SMR 700, which includes a sphericalexterior portion 720, an open-air cube corner retroreflector 710, acollar 905, and a reference mark, or feature, 930. In an embodiment, acavity in the spherical exterior portion 720 is sized to accept the cubecorner retroreflector 710. The cube corner retroreflector 710 is atleast partially disposed in spherical exterior portion 720, possiblywith adhesive. The collar 905 provides protection for the cube cornerretroreflector 710 and provides a convenient grip. The reference mark,or feature, 930 may be used to establish an orientation of the SMR inspace, as discussed in more detail hereinbelow. The reference feature930 may also be a textural feature such as a dimple or bump. It might bea serial number, a reflective region (as in 610 of FIG. 6A), a barcode(as in 630 of FIG. 6B), a radio frequency identification (RFID) tag, orother feature. In this case, the reference mark may be selected byconvention to be for example a center, a left side, or a right side of agiven feature. The reference feature may be any feature that enables theuser or a reading device to distinguish an orientation of theretroreflector 710. FIG. 5B shows a cross sectional view taken throughthe center of the SMR 700. The cross section reveals the open-air cubecorner 710 to be of the replicated type, but a cube cornerretroreflector formed of three mirror panels or directly formed usingECM could equally well be used. FIG. 5C shows a front view of the SMR700.

FIGS. 6A-C depict three embodiments of SMRs. In FIG. 6A, the SMR 700includes a spherical exterior portion 720, a cube corner retroreflector710, and a collar 905. A region of reflecting material 610 is placed onthe front surface of collar 905 in FIG. 6A. This region of reflectingmaterial 610 is illuminated by light from the laser tracker and itsposition determined by a locator camera disposed on the tracker. Forexample, the light might be provided by the light sources 54 and theimage of the illuminated SMR captured by one or more locator cameras 52as shown in FIG. 1. The position of the region 610 may be used to findan orientation of the SMR 700 as explained further hereinbelow. In FIG.6B, the SMR 700 includes the same elements as in FIG. 6A except that theregion of reflecting material 610 is replaced by a barcode pattern 630.The barcode pattern 630 may be a one-dimensional barcode pattern or atwo-dimensional barcode pattern. Two dimensional barcode patterns aresometimes referred to as matrix barcodes, 2D barcodes, 2D codes or bynames such as QR that indicate the specific form of the code. Thebarcode may serve to provide an identification of the SMR or to storeone or more parameters of the SMR as is described in more detailhereinbelow. The barcode 630 may also act as a reference mark (servingthe function of 930 in FIG. 5A) or as a region of reflecting material toprovide an orientation of the SMR 700. If desired, the barcode patternmay extend around the entire circumference of the collar lip rather thanonly a portion of the lip as shown in FIG. 6B. If desired, the type ofbarcode pattern known as a radial pattern may be used. In FIG. 6C, theSMR 700 includes the same elements as in FIG. 6A except that the regionof reflecting material 610 is replaced by an RF identification chip 650.This chip may be interrogated by an RF transmitter/receiver, which mightbe, for example, a handheld unit or a unit located on a laser tracker10, to obtain information about the SMR 700. This information may be aserial number or one or more parameters of the SMR 700.

FIGS. 7A, 7B show front view and side-sectional views of an SMR 700. TheSMR includes a spherical exterior portion 720 and a retroreflector 710.The retroreflector 710 is a cube corner retroreflector having threeplanar reflectors 825AB, 825BC, and 825AC that are mutuallyperpendicular and intersect in three intersection junctions 810A, 810B,and 810C and a vertex 820. In an ideal SMR the three intersectionjunctions are intersection lines and the vertex is a point. In thisapplication, the term line is often used to refer to an intersectionjunction even if the junction is not a perfectly straight and sharpline. Similarly the term vertex is often used to represent theintersection of region point of the three planes even if the actualregion of intersection is not a perfect point. The spherical exteriorportion 720 has a sphere center 860, which in general is at a differentpoint in space than the vertex 820.

An axis of symmetry 840 is symmetrical with respect to the threeintersection lines 810A, 810B, and 810C. The angle between the axis ofsymmetry and any of the three intersection lines is cos⁻¹(1/√{squareroot over (3)})=54.7°. A runout plane 865 that passes through the spherecenter 860 is drawn perpendicular to the axis of symmetry 840. The axisof symmetry 840 intersects the runout plane 865 in an intersection point870. An SMR error vector 885, which extends from the vertex 820 to thesphere center 860, decomposes into two vector components: an SMR deptherror vector component 880 that extends from vertex 820 to theintersection point 870 and an SMR runout error vector component 890 thatextends from the intersection point 870 to the sphere center 860. TheSMR depth error vector component 880 has a length equal to an SMR deptherror, and the SMR runout error vector component 890 has a length equalto an SMR runout error. The SMR depth error vector component 880 and theSMR runout error vector component 890 are shown in FIG. 7B, which is aside view of a cross section drawn through line A-A in the front view ofFIG. 7A. The SMR has an SMR frame of reference 730 that is fixedrelative to the SMR. An example of a possible SMR frame of reference isshown in FIGS. 7A, 7B. All of the elements of the SMR, including the SMRerror vector, the SMR depth error vector, and the SMR runout errorvector, are fixed relative to the SMR frame of reference. The SMR frameof reference may conveniently be placed at either the vertex point 820or the sphere center 860.

The elements of FIGS. 7A, 7B are shown in FIGS. 8A, 8B in perspectiveview. FIG. 8A shows a portion of the SMR 700 that includes the threeplanar reflectors 825AB, 825BC, 825AC, the three intersection junctions810A, 810B, 810C, the vertex 820, and the axis of symmetry 840. FIG. 8Bshows a magnified view of the region near the center of the SMR, withthe vertex 820 shown in line with the axis of symmetry 840. The runoutplane 865 is perpendicular to the axis of symmetry 840 and passesthrough the sphere center 860. The axis of symmetry intersects therunout plane at an SMR intersection point 870. The SMR error vector 885extends from the vertex 820 to the sphere center 860. The SMR deptherror vector 880 extends from the vertex 820 to the SMR intersectionpoint 870. The SMR runout error vector 890 extends from the SMRintersection point 870 to the sphere center 860.

FIG. 9A shows a portion 900 of an SMR that includes a collar 905 ontowhich is affixed a reference feature 910, which might be a serial numberor barcode, for example. In this example, the reference mark 930 isselected by convention as being in the center of the reference feature910. In another embodiment, the reference mark is a line 930 inscribedon the collar as in FIG. 5A. In another embodiment, the reference markis affixed directly to the spherical exterior portion 720. Associatedwith the reference mark 930 is a reference point 932. An SMR referenceplane 920 encompasses the reference point 932 and the axis of symmetry840.

A magnified perspective view near the center of the SMR is shown in FIG.9B. The vertex point 820 is shown in both FIGS. 9A, 9B. An SMR referenceray 940 is a ray coincident with the line of intersection between theSMR reference plane 920 and the SMR runout plane 865, wherein the SMRreference ray 940 begins at the SMR intersection point 870 and isdirected along the half of the SMR reference plane 920 that includes thereference point 932. The angle between the SMR reference ray 940 and theSMR runout error vector 890 is the SMR runout reference angle 950. Thenumerical value of the SMR runout reference angle of a particular SMR isa property of that SMR. In an embodiment, the SMR depth error, the SMRrunout error, and the SMR runout reference angle are determined for eachSMR by carrying out measurements as discussed hereinbelow.

FIG. 9C shows the same portion 900 of an SMR as in FIG. 9A. A beam oflight 46 from a device 10 intersects the vertex point 820. A beam deptherror vector 962 has a magnitude equal to the SMR depth error 880 andextends along the direction of the beam 46 from the vertex point 820 toa beam intersection point 970, as shown in FIG. 9D in a magnifiedperspective view near the center of the SMR. A beam runout plane 965includes the beam intersection point 970 and is perpendicular to thebeam depth error vector 962. A beam reference plane 975 encompasses thereference point 932 and the beam depth error vector 962.

A beam reference ray 972 is a ray coincident with the line ofintersection between the beam reference plane 975 and the beam runoutplane 965, wherein the beam reference ray 972 begins at the beamintersection point 970 and is directed along the half of the beamreference plane 975 that includes the reference point 932. The anglebetween the beam reference ray 972 and the beam runout error vector 976is the beam runout reference angle 982. To the extent that the beam oflight 46 is not aligned with the axis of symmetry 840, there will be adifference between the calculated 3D coordinates of the sphere center978 and the actual 3D coordinates 860 of the sphere center. Thisdifference is discussed further with reference to FIGS. 12A-E.

Measurements are performed on each SMR to determine the position of thesphere center relative to the vertex. The results of such measurementsmay be described in several different ways. One such description of thesphere center relative to the vertex point includes the SMR depth error880, the SMR runout error 890, and the SMR runout reference angle 950. Adifferent but equivalent description includes component lengths of theSMR error vector using Cartesian coordinates. For example, suchcomponent lengths may be given along Cartesian axes x, y, z within aframe of reference of the SMR such as the frame of reference 730 ofFIGS. 7A, 7B. Some alternative descriptions are now given. Othercoordinate systems are also possible, as will be clear to one ofordinary skill in the art.

FIG. 9B shows the frame of reference 40, which is fixed to the SMR asshown in FIG. 1. If the vertex 820 is taken as the origin in the frameof reference 40, the 3D coordinates of the sphere center (C) are givenin the frame of reference 40 as (x_(C), y_(C), z_(C)), where x_(C) isthe SMR depth error and y_(C), z_(C) are coordinates in the SMR runoutplane of an SMR runout error vector. In this case, the z axis is takenalong the direction of the SMR reference ray 940. An alternativeapproach is to use a frame of reference 988, for which the z′″_(C) axisis aligned to the position of maximum runout, which is to say that thez′″_(C) axis is aligned to the SMR runout error vector 890. In thiscase, the 3D coordinates of the sphere center (C) are given as (x′″_(C),y′″_(C), z′″_(C))=(x′″_(C), 0, z′″_(C)) since y′″_(C) is zero for thiscase. The frame of reference 988 may be realized by aligning thereference mark 930 to the position of maximum runout of theretroreflector.

A Cartesian frame of reference may also be applied to the beam runoutplane 965. FIG. 9D shows the frame of reference 996. If the vertex 820is taken as the origin in the frame of reference 996, the 3D coordinatesof the calculated sphere center 978 based on the direction of the beam(B) of light are given as (X_(B), Y_(B), Z_(B)), where X_(B) is the SMRdepth error along the direction of the beam of light (the X_(B) axis)and Y_(B),Z_(B) are coordinates in the beam runout plane of the beamrunout error vector. The magnitudes of the components Y_(B),Z_(B) arethe same as the magnitudes of the components Y_(C), Z_(C), only shiftedfrom the plane 865 to the plane 965. An alternative approach is to use aframe of reference 998, for which the Z′_(B) axis is aligned to the beamrunout error vector 976. In this case, the 3D coordinates of thecalculated sphere center (B) are given as (X′_(B), Y′_(B),Z′_(B))=(X′_(B), 0, Z′_(B)) since Y′_(B) is zero for this case.

There are many ways to find the position of the sphere center 860relative to the vertex 820. One method is to measure the SMR with aCartesian coordinate measuring machine (CMM). With this method, theposition of the vertex relative to the sphere center can be found to afraction of a micrometer. For example, with a very good Cartesian CMM,an expanded uncertainty of the position of the center relative to thevertex may be better than 0.4 micrometer along each of three Cartesianaxes x, y, z. This error is much less than the centering error of anSMR, which, in a typical SMR is 0.0005 inch=12.7 micrometers along theaxes x, y, z. In a very good SMR, the specified centering errorcomponents may be as small as 0.0001 inch=2.54 micrometers.

Another way to measure the depth of the sphere center 860 relative tothe vertex 820 makes use of an absolute interferometer or other type ofADM having a high accuracy. In an embodiment, a kinematic nestconfigured to repeatably center a spherically shaped object is arrangedto push upwards on an SMR. A reference SMR is measured with an accurateCartesian CMM to find the SMR error vector 885. The reference SMR isplaced in the nest and the absolute interferometer is used to measurethe distance along a horizontal line from the absolute interferometer tothe vertex of the SMR. An SMR under test is next placed in the nest andthe measurement repeated. Let the SMR depth error of the reference SMR,E_(DepthRefSMR), be taken as generally positive in the direction from adistance measuring device to the SMR. Then, following the aboveprocedure, the SMR depth error of a test SMR isE _(DepthTestSMR) =d _(TestSMR) −d _(RefSMR) +E _(DepthRefSMR),  (1)where d_(TestSMR), d_(RefSMR) are the measured distances to the SMRunder test and the reference SMR, respectively.

Another way to measure the SMR runout error and SMR runout referenceangle (or, equivalently, the Cartesian errors in the SMR runout plane)is to rotate an SMR under a microscope according to a method well knownin the art. A description of this method is given in Section B-2.1 ofAppendix B of ASME Standard B89.4.19-2006, Performance Evaluation ofLaser-Based Spherical Coordinate Measurement Systems, which isincorporated by reference herein. With this method, an SMR under test isplaced on a kinematic nest that rests on a microscope stand. A lightsource illuminates the frame of the microscope. The focus is adjusted toview a speck of dust (or other small object) on the microscope frame. Anoperator rotates the SMR about the sphere center within the kinematicnest and observes on the microscope the radius of the runout circle. Theobserved radius is divided by four to get the SMR runout error, which isthe magnitude of the SMR runout error vector 890. The procedurediscussed in this paragraph is used as a method of determining whetheran SMR meets it runout (centering) specifications. For example, amanufacturer may provide a specification for an SMR stating that the SMRhas a centering error of less than 0.0005 inch. This would beinterpreted to mean that the SMR has an SMR depth error of less than0.0005 inch and SMR runout error of less than 0.0005 inch. Although thedepth error and the runout error have been measured in the past forSMRs, provision has not heretofore been made to use these values by aprocessor to correct readings of device 10 based on SMR compensationparameters, the compensation parameters which might include SMR deptherror and SRM runout error vector component information.

The observed position of the SMR runout error relative to a referencemark on the SMR may be used to determine the SMR runout reference angle950. In an embodiment, discussed further with respect to FIGS. 19A, 19B,the reference mark 930 is aligned to the observed position of maximumrunout during the test procedure. The effect of this is to make the SMRrunout reference angle equal to zero. In an embodiment, a calibrationlaboratory technician places the reference mark 930 at the position ofmaximum runout. In other words, the laboratory technician places thereference point 932 within the reference plane 920.

Besides errors in SMR centering (SMR depth error and SMR runout errorvector component), there are also errors in SMR radius. In other words,the SMR radius is not exactly that indicated in a manufacturer'sspecifications. As an example, some high quality SMRs are manufacturedfrom grade 25 steel balls having a diameter tolerance of ±0.0001inch=±2.54 micrometers, which is equivalent to a radius tolerance of±1.27 micrometers. In other words, for an SMR manufactured with thistype of steel ball, the actual SMR radius is expected to lie within±1.27 micrometers of the nominal (specified) radius, at least atportions of the spherical surface not too close to the cavity that holdsthe retroreflector.

There are several ways to measure the radius of an SMR. A Cartesian CMMcan be used to accurately measure the radius of an SMR under test. Theradius error is found by taking the difference between the measuredradius and a reference or nominal radius.

An absolute interferometer may also be used to measure the radius errorof an SMR under test. With this method, a reference sphere (ball) ismeasured with a coordinate measuring instrument such as a Cartesian CMMor Talyrond® roundness measuring device to find the radius of thereference sphere. In an embodiment, a kinematic nest configured torepeatably center a spherically shaped object is arranged to pushupwards on a spherical surface. The reference sphere is placed in thenest and the absolute interferometer focused onto the sphere surfacealong a line normal to the surface. The absolute interferometer measuresa distance from the interferometer to the surface. An SMR under test isnext placed in the nest. The SMR is rotated to enable the beam from theabsolute interferometer to be collinear with a normal vector to thespherical exterior portion 720, and the absolute interferometer is usedto measure the distance. The difference between the measured distance tothe SMR under test and the measured distance to the test sphere is theradius error.

Changes in temperature of the SMR may cause the vertex 820 to shift itsposition relative to the sphere center 860. Such changes in SMRtemperature may result from (1) changes in the ambient temperature ofthe air surrounding the SMR, (2) heating of the SMR by the operator'shand, and (3) contact of the SMR with a relatively warm object such as ahome position nest 17 of a laser tracker 10 of FIG. 1.

With some types of SMRs, the effect of temperature may be relativelysmall. For example, as discussed hereinabove, one type of SMR is made ofa single piece of steel into which the three mutually perpendicularsurfaces are etched using ECM. With this type of SMR, the change in theSMR depth error with temperature will equal the coefficient of thermalexpansion (CTE) times the change in SMR temperature times the initialSMR depth error. If the initial SMR depth error is 0.001 inch=25.4micrometers and the SMR is made of steel having a coefficient of thermalexpansion of 11.5 micrometers/meter/° C., the change in the SMR deptherror over a 30 degree Celsius change in SMR temperature is(25.4×10⁻⁶)(11.5)(30) micrometer=0.009 micrometer, which is a negligibleamount.

With some other types of SMRs, the thermal effects are larger. Forexample, consider the type of SMR that includes an aluminum slug putinto a 1.5 inch (38.1 mm) diameter spherical exterior portion of steel.Suppose that the aluminum slug extends 10 mm below the vertex and isglued to the steel portion at that position. Neglecting the thermalexpansion of the glue bond and considering a point of contact at whichthe axis of symmetry intersects the spherical exterior portion, therelative change in the vertex position with temperature is thedifference in the CTE values for aluminum and steel times the 10 mmextension times the change in temperature. Suppose that the CTE of steelis 11.5 micrometers/meter/° C., the CTE of aluminum is 23micrometers/meter/° C., the depth extension is 10 mm, and the change intemperature is 30° C. The change in the vertex relative to the spherecenter is then (0.01)(23−11.5)(30) micrometers=4.45 micrometers.

To correct for the movement of the SMR vertex as a result of thermalexpansion, a temperature sensor such as a thermistor or RTD may beembedded in the SMR. In an embodiment shown in FIGS. 10A, 10B, 10C, asmall connector socket 1030 is disposed on or in the SMR 1000. Theconnector socket is attached through a collection of wires 1032(typically two or three wires) to the temperature sensor 1034. Thetemperature sensor 1034 might be a thermistor, RTD, thermocouple, orother device. A sensor cable 1040 includes a second collection of wires1044 attached to a first connector 1042 on one end of the cable 1040 andto a second connector 1046 on the opposite end of the cable. The firstconnector 1042 attaches to the connector socket 1030 and the secondconnector 1046 attaches to a temperature measurement system disposed ona laser tracker 10, computer 80, accessory box 70, temperature meter, orother device. Many types of temperature measurement systems may be used.A simple temperature measurement system (not shown) may includeelectronics based on a Wheatstone bridge having three internalresistors. A first internal resistor may be attached to a voltagesource, a second internal resistor attached to a ground, and theexternal temperature sensor 1034 and wires in cable 1044 providing afourth external resistive leg of the bridge. Such temperaturemeasurement systems are well known in the art. The temperaturemeasurement system converts observed voltages into a temperature of theSMR. Coefficients stored in memory may then be used to correct theposition of the vertex relative to the sphere center. The memory may beincluded in a laser tracker 10, computer 80, accessory box 70, or otherdevice. Measurements are carried out ahead of time for a particular typeof SMR to obtain information that describes SMR thermal expansioncharacteristics. In a simple case, a single CTE value or CTE value timesSMR depth error may be sufficient to describe the vertex movementrelative to the sphere center. For example, in the example given abovein which the vertex moves by 4.45 micrometers over 30 degrees Celsius,the single parameter might be used to give a value of 0.1483 for CTEtimes depth error, the value having units of micrometers per degreeCelsius. In another embodiment, a table of values or coefficients isprovided.

Use of an embedded temperature sensor 1034 with a sensor cable 1040 hasthe advantage of avoiding the need for a battery, temperature circuit,or wireless communications system within the SMR. With this system anSMR might be checked, for example, when the SMR is returned to a trackerhome position.

As shown in FIG. 10D, one possibility is to attach the cable 1040through socket 1052 to temperature electronics module 1050. In anembodiment illustrated in FIG. 10E, a battery 1054 provides electricalpower over wires 1062 to the embedded temperature sensor 1034,temperature processing electronics 1056, and wireless communicationselectronics 1058. In an embodiment, the temperature processingelectronics 1056 includes a Wheatstone bridge, resistors, and amicroprocessor to provide a digital signal through wire 1064 to wirelesscommunications electronics 1058. The digital signal represents atemperature measured by the temperature sensor 1034. In an embodiment,the wireless communications electronics 1058 launches a digitalrepresentation of the measured temperature over antenna 1059. In anembodiment, the wireless communications electronics is configured tosend the digital representation over antenna 1059 at regular intervals,for example, every five minutes. The interval time may be selected toprovide adequate temperature information while saving battery power. Thewireless signal from the antenna 1059 may be received by electronicswithin a device 10 shown in FIG. 1 and the received temperature valuesused to improve compensation of the 3D coordinates of the SMR spherecenter. In an embodiment, the temperature electronics module 1050 may beplaced in a pocket of the operator—for example, a shirt pocket ortrousers pocket.

In an embodiment shown in FIG. 10F, the temperature processingelectronics 1050 may be affixed to the wrist of an operator. In anembodiment, the operator wears a glove 1070 into which the temperatureprocessing electronics 1050 and the cable 1040 are integrated. In anembodiment, the glove is an insulating glove to minimize the transfer ofheat from the operator's hand to the SMR 1000. In another embodiment,the glove is not an insulating glove but has finger openings to permitdirect handling of the SMR by the operator. In another embodiment, theoperator does not wear a glove. Instead temperature processingelectronics 1050 is attached directly to the operator's wrist, forexample, by means of a strap or elastic band.

FIG. 11 shows an interface component 1120 attached to an SMR 1100.Interface component 1120 may contain a number of optional elements. Theinterface component 1120 may be connected to a temperature sensormounted within the SMR 1100. Antenna 1130 may be used to send and/or toreceive wireless data in the form of radio frequency signals. Such anantenna may be attached to a small circuit board powered by a smallbattery 1128 that fits inside interface component 1120. The smallcircuit board may be made of rigid-flex material which permits a verycompact circuit to be enclosed within the interface component. Byproviding a temperature sensor and wireless communication system poweredby a battery, the temperature of the SMR may be known at all times sothat the measurements of the 3D coordinates of the SMR 1100 are asaccurate as possible.

Numerical values used to compensate for imperfections in SMRs as a wayof enabling more accurate 3D measurements are referred to as SMRcompensation parameters. SMR compensation parameters are typicallystored in memory of a measurement device or a computing device. Forexample, SMR compensation parameters may be stored in a memory of thelaser tracker 10 of FIG. 1. A processor within the laser tracker 10 maybe used to correct the 3D coordinates of the sphere center of SMR 26.Alternatively, a processor within an external computer 80, an accessorydevice, or a networked computing device may be used to accesscompensation values stored in memory and use these values to correct the3D coordinates of the sphere center. Such compensations may account fordifferences in the position of the vertex relative to the sphere center.Such compensations may also account for the effect of errors in thesphere radius using methods described hereinbelow with respect to FIGS.14-17.

In some cases, compensation calculations are made within a processor ofa measurement device such as a laser tracker. For example, the trackerprocessor may identify the SMR being used for a particular measurementand automatically perform compensation calculations for that SMR totransform the measured vertex 3D coordinates to sphere center 3Dcoordinates. In other cases, compensations are made by applicationsoftware. For example, application software may consider the positionand orientation of the SMR in making a plurality of measurements andapply compensation calculations for the SMR radius to eliminate errors.In general, the term processor may be understood to mean a processor ina device such as a tracker, a processor in an external computer, or aprocessor in both.

There are several ways by which SMR compensation parameters can beentered into memory. In an embodiment, SMRs shipped with the device 10from the factory come with compensation parameters pre-loaded intomemory. In another embodiment, the user is provided with a list ofnumerical compensation values for each SMR. Application softwareembedded within the device 10 provides a means by which the user mayenter the numerical values. Such values need only be entered once, asthey are stored in memory within the device 10. In another embodiment,the SMR compensation parameters are provided on a flash drive, CD ROM,or other medium read by device 10, computer 80, or other component forautomatic storage in memory. In another embodiment, numerical values forcompensation parameters are downloaded into the tracker over a network.In another embodiment, SMR compensation parameters are encoded into aone-dimensional or two-dimensional barcode 630. A barcode reader mayread the SMR compensation values on the barcode and automaticallydownload these into memory in the device 10.

In an embodiment, a close-range camera 56 shown in FIG. 1 is pointeddirectly at an SMR when the device 10 locks onto (begins tracking) anSMR in one of the home nests 17. In the device 10 of FIG. 1, the camera56 is placed above the aperture through which the light beam 46 isemitted. To ensure that the camera can clearly read an SMR barcode, thecamera assembly may be pointed toward the center of an SMR placed in ahome position 17. In other words, for the case shown in FIG. 1, theoptical axis of the camera may be pointed slightly downward ratherparallel to the beam of light 46. In addition, in an embodiment, thecamera 46 is configured to focus clearly on an SMR in a home nest 17.This is generally different than for the cameras 52, which areordinarily designed to focus on retroreflectors relatively far from thetracker. In an embodiment, the camera 56 has a small enough field ofview to provide adequate resolution for a bar code or serial number. Forexample, the field of view for such a camera might be about 20 degrees.The small field of view and clear focus at the home position may beobtained by correctly selecting the focal length and adjusting theposition of the lens in the camera 56. The combination of optimumpointing direction (toward the home positions 17), in-focus condition atthe home position 17, and relatively small field of view ensure that arelatively inexpensive camera 56 can clearly resolve the marks on abarcode 610, which might be a one-dimensional or two-dimensionalbarcode, for example. Furthermore any lights near the SMR are turned offduring the operation of the camera 56 to ensure that the cameraphotosensitive array is not blinded by a bright retroreflected light.Ordinarily any lights need to be located at least one retroreflectordiameter away from the edge of the retroreflector to prevent thisblinding effect. In other words, if the retroreflector is an open aircube corner retroreflector having a circular cross section and adiameter of one inch, any lights should be located at least one inchfrom an outer edge of the retroreflector. Because the laser beam 46leaving the tracker is collimated and strikes the retroreflector in thecenter, in most cases, little light will scatter back into the camera56. However, it the laser beam 46 is too bright, it can be turned offduring the reading of the barcode on the SMR. In an embodiment, thecamera 56 is used in combination with optical character recognition(OCR) software to read a serial number.

Inasmuch as the resetting of SMR distance at the home position isroutine, a measurement of the barcode on the SMR can be made inconjunction with the home position measurement without requiring extrasteps on the part of the operator. In an exemplary method, the SMR isplaced in the home position. The tracker first turns on the camera toview the barcode and extract the SMR parameters. It then turns on thebeam of light, sends it to the vertex, measures the distance, and resetsthe distance to a home reference value. To reset the distance meter tothe home reference value in the most accurate possible way, in anembodiment, software within the tracker sets the distance value to beapplied at the SMR sphere center rather than the vertex point. This isimportant because it ensures that the home reference value is correctlyapplied for all SMRs, regardless of the SMR depth error. To determinethe sphere center as accurately as possible, the SMR should be placed ina preferred orientation within the home position nest 17 or the camera56 should be used to automatically determine the orientation of the SMRin the home position nest. These methods of establishing the position ofthe SMR in the home position nest are discussed in more detailhereinbelow. In FIG. 17, there are three different home position nestssized to accommodate three differently sized SMRs. In an embodiment, theSMRs are sized to accept SMRs having diameters of 1.5, 0.875, and 0.5inch. A different home reference value is provided for each of thesehome position nests.

In an embodiment, SMR compensation parameters are encoded into an RFIDtag 650. The encoded information is retrieved using an RFID reader,which may be attached to the payload 12, perhaps in place of theclose-range camera 56. The retrieved serial number may be used to accessthe SMR data from a networked system (the Cloud) or from a database ofinformation saved within a device such as a tracker or computer.

In the general case, a 3D coordinate measurement device such as lasertracker 10 obtains measured 3D coordinates of the SMR vertex, forexample, by measuring a distance and two angles to the SMR. The SMRcompensation factors are applied to the measured 3D coordinates of thevertex to obtain the 3D coordinates of the sphere center using methodsnow described. In making a measurement, the operator holds the referencepoint 932 so as to place the SMR reference plane 920 in a preferredorientation. A preferred orientation may be selected in severaldifferent ways, depending on the measurement objectives.

In general, the operator will endeavor to align the axis of symmetry tothe direction of the beam of light from the device. This was discussedhereinabove in reference to FIGS. 12, 13. The term preferred orientationas used herein refers to a positioning of the reference point as anadditional step in the alignment procedure. A way to achieve thepreferred orientation while leaving the axis of symmetry aligned withthe beam of light is to rotate the SMR about the axis of symmetryfollowing the aligning of the axis of symmetry to the beam of light.Since the SMR reference ray is perpendicular to the beam of light and isin the reference plane that includes the reference point, we may saythat by turning the axis of symmetry, the operator adjusts the SMRreference ray to obtain the preferred orientation.

There are some special cases in which it is not possible to align theaxis of symmetry to the beam of light. For example, with the SMR at thehome position 17, it may not be possible to align the axis of symmetryto the beam of light because of mechanical constraints. In this specialcase, the meaning of the term preferred orientation is modifiedaccordingly to permit for the necessary change in alignment. The specialcase for alignment at the home position is discussed hereinbelow.

A first type of preferred orientation is one in which the SMR referenceplane 920 is aligned to the x″-z″ plane of the payload frame ofreference 35 as shown in FIG. 1. The x″ axis corresponds to thedirection of the beam of light, and the z″ axis is perpendicular to thex″ axis and to the y″ (zenith) axis. The x″-z″ plane always includes thez′ vector (of the device frame of reference 30), which points out thetop of the device 10. For the device 10 in its normal upright position,the preferred orientation is one in which the SMR reference planecontains a gravity vector as well as the beam of light 46. However, themore general x″-z″ plane can be used when the gravity vector may not beappropriate, for example, when the tracker is turned on its side withthe laser beam pointed straight up. With the first type of preferredorientation, the operator simply holds the SMR so as to place the SMRsphere center and the SMR reference mark in the plane that includes thebeam 46 and the axis z′. The operator should also attempt to align theaxis of symmetry 840 of the SMR to the direction of the beam of light46, as discussed hereinabove with respect to FIGS. 9C, 9C andhereinbelow with respect to FIGS. 12, 13. With the SMR held in thepreferred orientation, software in the processor uses the measured 3Dcoordinates of the SMR vertex and the SMR compensation parameters tocalculate the SMR sphere center, as described hereinabove with respectto FIGS. 9A-D.

A second type of preferred orientation is one in which the SMR referenceplane 920 is aligned to the y″-z″ plane of the payload frame ofreference 35 as shown in FIG. 1. The y″-z″ plane always includes thezenith axis 18 (y″ axis) of the device 10. If the device 10 is placed inan upright orientation as shown in FIG. 1, the azimuth axis 20 ispointed in the vertical direction, and the zenith axis 18, which rotatesabout the azimuth axis, lies on a horizontal plane. With the second typeof preferred orientation, the operator holds the SMR so as to place theSMR sphere center and the SMR reference mark in a plane that includesthe beam 46 and the zenith axis 18 (x″ axis). If the reference mark 930points radially outward on a collar 905 as shown in FIG. 9A, then, forthe second preferred orientation, the reference mark should be held in ahorizontal plane. For the second type of preferred orientation, apreferred position of the SMR reference mark 930 relative to the spherecenter 860 needs also to be given—for example, to the right of thesphere center. As stated hereinabove, the operator should attempt toalign the axis of symmetry 840 of the SMR to the direction of the beamof light 46.

A third type of preferred orientation is one in which the SMR referenceray 940 is aligned in a prescribed manner to a measurement line tomeasure a dimensional characteristic of the measurement line. This isdiscussed further hereinbelow with reference to FIGS. 19A, 19B.

We now discuss with regard to FIGS. 12A-E errors associated withmisalignment of the axis of symmetry 840 with respect to a beam of lightfrom a device 10. An SMR in FIG. 12A receives a beam of light 1210having a beam center 1212 and a beam width 1214, the beam of light 1210beginning to be clipped by a collar 905 of the SMR. The angle 1215 isthe acceptance angle of the SMR for the beam of light 1210. For an SMRthat has a diameter of 1.5 inches and receives a typical beam of redlight from a laser tracker 10, the acceptance angle 1215 is usuallyabout 25 degrees.

An SMR in FIG. 12B receives a beam of light 1240 that is in line withthe axis of symmetry 840. For FIG. 12B, an expanded region 1230 near thevertex 820 and sphere center 860 is shown in a magnified view 1 in FIG.12C. Because the beam of light 1240 is aligned with the axis of symmetry840, the position of the sphere center may be determined with accuracyonly limited by the measurement error in finding the 3D coordinates ofthe SMR vertex—in other words, by the errors in the distance and twoangles measured by the device 10.

The SMR 720 in FIG. 12D has been rotated about its sphere center by anangle of 10 degrees. As a result of this rotation, the vertex 820 shiftsby an amount 1250 to a new vertex position 820R. The axis of symmetry,which is the axis that is symmetrical with respect to the threeintersection junctions, also shifts by 10 degrees from the line 840 tothe line 840R. As a result, rotating the SMR 720 about its center, forexample, when the SMR is placed on a kinematic nest, results in amisalignment error vector 1250 in the position of the center aftercompensation parameters have been applied for the SMR depth error vectorand the SMR runout error vector. As shown in FIG. 12E, the misalignmenterror 1250 includes a component 1252 along the axis of symmetry 840R anda component 1254 on a plane perpendicular to the axis of symmetry 840R.

During normal operation, an operator can usually keep the axis ofsymmetry 840 of a 1.5-inch diameter SMR aligned to the direction of thebeam of light 1240 to within about 10 degrees. As shown in FIG. 12D, arotation of an SMR about a sphere center 860 by an angle of 10 degreesresults in a misalignment error vector 1250 that is relatively smallcompared to the SMR error vector 885R. For the case of the 3Dcoordinates of the SMR being measured by a laser tracker, the beam oflight 1240 is the beam 46 as shown in FIG. 1.

Referring now to FIGS. 13A-F, methods are described to improve thealignment of the axis of symmetry 840 with the beam of light 46, therebyminimizing the magnitude of the misalignment error vector 1250. In afirst method shown in FIG. 13A, an alignment cap 1310 is placed over thecollar 905. The alignment cap includes a ring 1312 onto which isattached an opaque cover 1314 on which is centered marked crosshairs1317 or a marked circle 1316 having a diameter approximately the same asthe light beam 46 from the 3D coordinate measurement device 10. To alignthe axis of symmetry 840 with the incoming beam of light 46, theoperator first blocks the beam of light with the alignment cap 1310,which stops the beam from tracking the SMR 700. The operator places thealignment cap 1310 over the collar 905 and rotates the SMR to center theincident light beam 1318 in the marked circle 1316. The operator removesthe alignment cap 1310, which causes the beam to lock onto the SMR. Inso doing, the light beam 46 is brought into coincidence with the axis ofsymmetry 840. With this method, an alignment accuracy of 2 degrees orbetter might be expected for a 1.5-inch SMR.

In a second method shown in FIG. 13B, a window 1320 that lets lightthrough to the retroreflector is positioned against the collar 905 so asto align outer marked circle 1324 with the outer edge of the collar. Theoperator notes the position of incident light 1328 scattered off thewindow 1320 relative to crosshairs 1317 or an inner marked circle 1326and rotates the SMR to bring the incident light 1328 into coincidencewith the inner marked circle 1326. In so doing, the incident light beam46 is brought into coincidence with the axis of symmetry 830.

FIG. 13C illustrates a method of aligning the SMR by observing a portion1332 of the incident light beam with a reflective strip 1320, whichmight be a strip of cardboard, for example. By moving the strip inrelation to the aperture of the SMR, the operator can visually judge thedirection in which the SMR should be rotated to improve alignment.

FIG. 13D is like FIG. 13C except that a finger 1340 rather thanreflective strip 1330 is used to observe a portion 1342 of the incidentlight. By moving the finger in relation to the aperture of the SMR, theoperator can visually judge the direction in which the SMR should berotated to improve alignment.

In a method shown in FIG. 13E, a reflective cap 1350 is placed over thecollar 905, which is hidden from view in FIG. 13E. The reflective capincludes a ring 1352 onto which is attached a mirror 1354 designed toreceive light 1352 and reflect light 1353 off the mirror's frontsurface. Optionally, crosshairs 1317 or a marked circle 1356 is centeredon the minor 1354. The circle has a diameter approximately equal to thatof the light beam from the 3D coordinate measurement device. To alignthe axis of symmetry 840 with the incoming beam of light 1352, theoperator first blocks the beam of light with the reflective cap 1350,which stops the beam from tracking the SMR 700. The operator places thereflective cap over the collar 905 and, if the circle 1356 is present,rotates the SMR to place the beam approximately in the center of thecircle. The operator observes the position of the reflected light on ornear the 3D coordinate measurement device and, if needed to furtherimprove alignment, rotates the SMR 700 to move the reflected beam oflight closer to the emission point from the 3D coordinate measurementmachine. In FIG. 1, the emission point of the laser tracker 10 is thepoint at which the beam of light 46 leaves the laser tracker 10. Whenthe reflected beam of light is close enough to the emission point, theoperator removes the mirror cap 1350, which causes the beam to lock ontothe SMR. A typical high quality minor has a wedge angle of only a fewarc minutes, which produces a negligible angular deviation in thereflected beam of light. By reflecting the beam of light so that itstrikes the 3D measurement device near the emission point, it ispossible to align the axis of symmetry 830 with the beam of light towithin a small fraction of a degree. For example, an SMR 700 withreflective cap 1350 is 10 meters from a laser tracker 26, the axis ofalignment 840 is aligned to the emitted light beam 46 to within 1 degreeif the reflected laser beam is within about 175 mm, or about 7 inches,of the emission point.

FIG. 13F illustrates a method of causing the 3D coordinate measurementdevice, such as laser tracker 10, to emit a beam of light in a rotatingpattern 1360 having a diameter equal to that of the SMR, for example,SMR collar 905 or similar feature. The operator aligns the SMR byrotating it until the SMR is aligned to the rotating beam.

Previously in reference to FIGS. 1 and 6, a method was taught forcombining a home position measurement with a reading of barcodes using adevice camera. A part of this method was setting the distance meter to ahome reference value for the sphere center rather than the vertex of theSMR being used. To convert 3D coordinates from a vertex point to asphere center, it may be important to know the orientation of the SMR inthe home position, as described hereinbelow with reference to FIG. 22.Two methods are now given for establishing the orientation of the SMR.

As explained hereinabove, establishing a preferred orientation has twoaspects. In the usual case, the axis of symmetry of the SMR is alignedas well as possible to the beam of light. In a second aspect, the SMR isrotated about the axis of symmetry to place the reference mark in apreferred orientation.

In some cases, it is not possible to completely align the axis ofsymmetry to the beam of light. For example, at a home position 17 and atsome kinds of nests, mechanical constraints may prevent the SMR frombeing rotated into exact alignment with the beam. In the case of thehome position, another type of alignment criterion may be given. Forexample, a manufacturer may specify that the collar of an SMR is to beplaced approximately 2 mm above the nest. The software in the device 10may then calculate the error vector based on the provided SMRparameters.

For the case in which the axis of symmetry is not aligned with the beamof light, the orientation is easily obtained by moving the referencepoint into the desired orientation (for example, into a vertical planeor a plane that includes the azimuth axis) and then aligning the axis ofsymmetry in relation to the beam direction as specified (e.g., by movinga collar 2 mm above a nest). Another possibility is to use the camera 56to determine the orientation of the SMR. With the camera turned to pointat the home position, the orientation of the SMR is easily found fromthe position of the barcode (or any other marker). Use of the camera inthis way provides accurate results and is simple for an operator.

This camera concept may also be applied for the case of SMRs located atdistances of many meters from the device 10 if suitable zoom cameras areprovided in the camera. An example of such a zoom camera is described inthe '758 patent, discussed above and incorporated by reference. Areflective mark such as the mark 610 of FIG. 6A of the presentapplication may be used with such a camera to provide automaticdetermination of the orientation of an SMR. This method is applicablewhen a six DOF tracker is used with a three DOF SMR.

An SMR may be used to measure the coordinates of surface points bybringing the SMR into contact with the surface at a plurality of points.It may also be used to measure the coordinates associated with kinematicnests. In both of these types of measurements, an error in the radius ofthe SMR can produce an error in the measurements of surface or nestpoints. As explained hereinabove, methods are available to accuratelymeasure the radius of an SMR. The radius delta, defined as the measuredradius minus the nominal radius, may be stored in memory for lateraccess. The measured radius in this case is measured by one of theaccurate methods described hereinabove, for example, by using aCartesian CMM, Talyrond®, or absolute interferometer. The radius deltamay also be saved in an information storage device such as a barcode orRFID chip, which in an embodiment is attached to each SMR, and read by areading device of the 3D coordinate measurement device.

For a device 10 used to measure 3D coordinates on a surface with an SMR,the SMR is moved to several locations on the surface, and a collectionof 3D coordinates for the sphere centers of the SMR obtained for thecorresponding surface contact points. 3D center coordinates in closeproximity to one another are used to obtain a vector normal to thecollection of 3D points. The normal vector is projected from one pointin the collection of contact points or from one point not in thecollection but near the collection of points. The 3D coordinates of thecontact point corresponding to the one point are obtained by projectingthe normal vector from the 3D sphere center coordinates toward thesurface being measured.

An error in the radius of the SMR will not change the overall shape of aplanar surface. However, an error in the radius of an SMR can causeerrors in other situations. This can readily be seen by considering thecase in which an SMR is used to measure the distance between two planarsurfaces, wherein one planar surface is to the left of the SMR and oneplanar surface is to the right of the SMR. If the true diameter isgreater than the nominal diameter or reference diameter and if all othermeasurements are perfect, then the measured distance will be too smallby twice the SMR radius error.

An error in SMR radius can also produce errors in measurements made onsupports such as kinematic nests. FIG. 14A shows an example of a type ofkinematic nest 1400, which in this case includes three spherical balls1420 each affixed to a top surface 1412 of a base 1410 and separatedfrom the other balls by 120 degrees. A support axis 1430 is an axisperpendicular to the plane that intersects the centers of the threeballs 1420. The support axis 1430 is also equidistant from the centersof the three balls 1420 at any point along the support axis. FIG. 14Bshows an arrangement 1450 in which a spherical exterior portion of anSMR 700 is placed on the kinematic nest 1400. As used herein, the term“kinematic” means that the SMR can be removed from and returned to thenest, with the 3D coordinates being nearly the same after the movementas before the movement. As the SMR 700 is rotated, the sphere centerremains fixed in place on the support axis 1430. In some cases, a magnetis included in the base 1410 to hold a steel spherical exterior portionof an SMR firmly against the kinematic nest 1400 and to keep it fromfalling off the nest.

A way to describe the support axis 1430 in mathematical terms is as alocus of sphere centers for spheres of different sizes mounted on thenest. In other words, a sphere with a relatively small radius and asphere with a relatively large radius will both lie on the support axis1420. Of course, there is some minimum and maximum sphere size that willproperly fit onto the three balls 1420, but within the acceptable rangeof sphere sizes, the locus of sphere centers will lie on the supportaxis 1430.

SMRs are provided by manufacturers with a nominal radius. Applicationsoftware performs calculations based on the nominal radius of an SMR,the nominal radius being a numerical value provided by the SMRmanufacturer. Differences in values for the nominal radius and theactual radius can result in errors, as is discussed further hereinbelow.

A nest, such as nest 14A, does not in general have a clearly definedreference point. A convenient and consistent reference point for acombination of a particular nest with a particular SMR is an “idealsupport position,” which is a position on the support axis 1430. Theideal support position is defined as the position on the support axis1430 of the sphere center for a sphere having a radius exactly equal tothe nominal radius. An SMR having a radius different than the nominalradius will have a sphere center at a different position on the supportaxis referred to as the actual support position.

Because neither measurement of a radius nor corrections to 3Dcoordinates based on radius error depend on the internal reflectingmechanism of the retroreflector, the methods for correcting radiusdiscussed herein are not limited to an SMR having an open-air cubecorner retroreflector. The methods are equally applicable to an SMR thatincludes a glass cube corner retroreflector, which is to say, aretroreflector that includes a glass prism having three perpendicularreflecting faces. The methods are also applicable to the case of acateye retroreflector in which the retroreflector has a glass opticalelement shaped either as a single sphere or as two hemispheres cementedtogether, wherein the optical element is placed at least partiallywithin a cavity in a spherical exterior portion. SMRs that include glassprism or cateyes are well known in the art.

As stated hereinabove, the measured radius minus the nominal radius isthe radius delta. Let the support axis 1430 be positive in a directionfrom a plane connecting the centers of the three spheres to the spherecenter of an SMR held by the nest. In other words, in FIG. 14A, thedirection to the right is considered positive along the support axis1430. Then the ideal support position may be found by measuring the 3Dcoordinates of the sphere center of an SMR in the nest 1400 andtranslating the 3D coordinates along the support axis in the negativedirection by a distance approximately, but not exactly, equal to radiusdelta. The exact amount of translation also depends on the geometry ofthe nest 1400, as explained hereinbelow with reference to FIG. 15. Aformula may be used to determine the ideal support position as afunction of the radius error or delta. Compensation values such ascoefficients may be stored in memory for use by the processor, in thedevice 10 or a separate computer 80, for example, may be used indetermining the 3D coordinates of the ideal support position.

The amount of shift in the sphere center 860 is now calculated for thecase of an SMR 700 supported by a kinematic nest 1400 having three balls1420 separated by 120 degrees. FIG. 15 shows line segments correspondingto elements of the nest 1400 and SMR 700 of FIG. 14B. Each of the threespheres 1420 has a center 1510, with any two of the centers 1510separated by a base distance 1525, which is given a mathematical symbola. A cross section drawn through the centers of each ball shows anoutline 1515. Each of the balls contacts the spherical exterior portion720 of the SMR 700 at a tangent point 1520. A line drawn from the spherecenter 860 through a tangent point 1520 passes through the center 1510of a ball 1420. The SMR has a reference or nominal radius R and a radiuserror e so that the actual radius of the SMR is R+e. The three lines1525 form base of a triangular pyramid 1540. The lines 1530, whichextend from the ball centers 1510 to the sphere center 860, form theedges of the triangular pyramid. The radius of each ball is r so thatthe edges of the triangular pyramid have length R+e+r. The altitudesegment 1550 of the pyramid, which has a height h, extends from a basecenter 1545, which lies on the plane connecting the three ball centers1510, to the sphere center 860. Each of the vertices 1510 of the basehas an angle of 60 degrees, and so a line drawn from a ball center 1510to the base center 1545 has length b=a/√{square root over (3)}. By thePythagorean Theorem, the height of the altitude segment is h=√{squareroot over ((R+e+r)²−b²)}. Let the edge length be R₀ and the height be h₀for a radius error of e=0. Using the binomial approximation, it can beshown that, to good accuracy, the change in the height h as a result ofan error e is δh=eR₀/h₀. Because the height h₀ is smaller than the edgelength R₀, the change in height δh is somewhat larger than the radiuserror e. For example, for a radius error of 1 micrometer, the change inheight δh is 1.048 micrometers. The reason that the change in height islarger than the radius error is that a larger SMR 700 intersects theballs 1420 slightly farther away from the base that connects the ballcenters 1510.

In general, the change in height δh depends on the construction(geometry) of the SMR nest 1400 and is different for different types ofnests. In order to correct as accurately as possible for the effect ofthe radius error on the change in height, it is necessary to know boththe amount of radius error and the type of nest being used with the SMR.To get an approximate correction for the effect of the radius error onthe change in height, the radius error e may be used without consideringthe geometry of the nest. For the example given in the last paragraph,the relative error in the calculated height resulting from notconsidering the geometry of the nest 1400 was 4.8%.

An example is now given of the effect of SMR radius errors onmeasurements made with SMRs in nests. FIGS. 16A, 16B show front and sideviews, respectively, of a first SMR 700A and a second SMR 700B held by afirst nest 1400A and a second nest 1400B, respectively. In an ideal casein which the radius of both 700A and 700B is equal to the referenceradius, the length between the SMR centers is indicated in FIG. 16C bythe arrow 1672. Consider next a case in which the sphere radius of thefirst SMR 700A is equal to the reference radius while the sphere radiusof the second SMR 700B is larger than the reference radius. For the SMR700B, the sphere center is pushed upwards, as indicated by the arrow1674. Consequently, the measured 3D coordinates lead to the vector 1676.If the length of the vector 1672 is L₁ and the length of the vector 1674is δh, then the difference in the lengths 1672 and 1676 is ΔL=√{squareroot over (L₁ ²+δh²)}−L₁, which after applying the binominalapproximation, is given to good accuracy as ΔL=δh²/2L₁. Taking as anexample δh=2 micrometers and L₁=2 meters, the resulting error is 10⁻⁶micrometers, which is negligible.

In contrast, FIGS. 17A, 17B show the situation in which the first SMR700A and first nest 1400A are aligned as in FIG. 16B, while the secondnest 1400B is oriented perpendicular to the line connecting the spherecenters of 700A, 700B. In an ideal case in which the radii of both 700Aand 700B are equal to the reference radius, the length between the SMRcenters is indicated in FIG. 17B by the arrow 1752. Consider next a casein which the sphere radius of the first SMR 700A is equal to thereference radius while the sphere radius of the second SMR 700B islarger than the reference radius. For the SMR 700B, the sphere center ispushed to the left, as indicated by the arrow 1754. Consequently, themeasured 3D coordinates lead to the vector 1756, which is too short bythe offset value 1754. The offset value 1754 depends both on the delta(or radius error) and on the geometry of the nest, as explainedhereinabove. In this case, if the sphere radius of 700B is too large by2 micrometers and the nest geometry is the same as that given in theprevious example, the measured distance between the two SMRs will be toosmall by 2.096 micrometers. In other words, for the situation in FIGS.16A, B, the error in the measured length between the SMRs was notaffected by a diameter error in one of the SMRs while, for the situationin FIGS. 17A, B, the error in the measured length between SMRs isdirectly affected by a diameter error in one of the SMRs.

It is clear from the discussion hereinabove that in many situations thedirection of the support axes 1430 of two nests can have a large effecton the uncorrected distance measured between SMRs placed in the nests.There are several ways that a direction of a support axis 1430 can beobtained. First, the operator may indicate the direction of the supportaxis in application software. Second, a nest may be mounted directly onan object having surfaces known in a CAD model, from which the directionof the support axes 1430 may be determined. Third, measurements may bemade to an inspection plan that includes the direction of the supportaxis 1430 of each nest used in the inspection. Fourth, the operator maymeasure features of the nest to determine the direction of the supportaxis 1430. For example, in the case of the nest 1400 of FIG. 14A, theoperator may use the device 10 with an SMR to measure 3D coordinates ofpoints on the top surface 1412. These 3D point coordinates are fit to aplane from which the perpendicular support axis 1430 is found.

In general, to correct for errors for measurements made with SMRs placedin nests, both the direction of the support axis 1430 and the magnitudeof the radius delta is needed. A more accurate correction is possible ifthe geometry of the nest is also taken into account as discussed withreference to FIG. 15.

A procedure described with reference to FIG. 18 is useful whenever thesame SMR positions must be measured with a tracker moved to multiplelocations. For example, a calibration procedure may require that adistance between two SMRs 700A, 700B be measured with the tracker setaway from the SMRs by two different locations 10A, 10B as shown in FIG.18. In other cases, the tracker may be required to measure three or morenests from multiple locations as a way of putting tracker measurementsmade from different locations into a common frame of reference.

In a first step of a method, two or more SMRs 700A, 700B are rotated insupports 1400A, 1400B to align the axis of symmetry 840 of each SMR to a3D measurement instrument located at a first position having 3Dcoordinates (x₁, y₁, z₁) within a frame of reference 1810. At this firstposition, the tracker is given reference number 10A. This alignment maybe achieved, for example, using one of the alignment methods of FIGS.13A-F. The tracker at 10A measures the SMRs 700A, 700B and at least oneadditional retroreflector 700C, which need not be aligned to the tracker10A. In a second step, the same 3D measurement instrument is designatedas 10B when located at a second position having 3D coordinates (x₂, y₂,z₂). In this step, the SMRs 700A, 700B are not further rotated but leftin their initial orientations. The tracker 10B measures the 3Dcoordinates of the vertex of 700A, 700B, and 700C. The 3D coordinates ofthe vertices of SMRs 700A, 700B as measured by the 3D measurementinstrument 10B are mathematically corrected to account for themisalignment of the vertex 820 with respect to the sphere center 860 ofeach of the SMRs 700A, 700B.

The mathematical method for doing this is easy to understand. Using themeasured values for the retroreflector vertices for 700A, 700B, 700C,the tracker 10B is put into the frame of reference of the tracker at10A. This is done using optimization methods in which the six degrees offreedom (for example, x, y, z, pitch, roll, yaw) of tracker 10B areadjusted until the 3D coordinates for 700A, 700B, and 700C measured bytracker 10A and 10B match as closely as possible. The usual optimizationmethod is one in which the sum of the squared residual errors isminimized.

The transformation matrix needed to 3D coordinates measured by 10B intothe frame of reference of 10A can be used to transform the SMR errorvectors for 700A, 700B in 10A into the error vectors for 700A, 700B in10B. In this way, the step of realigning the SMRs 700A, 700B prior tomeasurement by tracker 10B can be eliminated.

It should be understood that the method of establishing a transformationmatrix by measuring the 3D coordinates of at least three retroreflectortargets from at least two locations may be carried out even in theabsence of SMRs. In other words, cube corner retroreflectors or othertypes of retroreflectors may be affixed to any sort of object. It shouldalso be understood that the method described herein may be used tocorrect the 3D coordinates of a single SMR or multiple SMRs when viewedfrom two or more stations.

As explained hereinabove, a type of preferred orientation of an SMR isone in which the SMR reference ray 940 is aligned in a prescribed mannerto a measurement line as a way of minimizing error in measuring adimensional characteristic associated with the measurement line. A caseis now considered in which the dimensional characteristic of interest isa length between two points.

In a measurement shown in FIGS. 19A, 19B, nests 1400A, 1400B have SMRrunout reference angles 950 of zero. The nest 1400A is mounted directlyabove the nest 1400B, and a 3D coordinate measurement device such astracker 10 is used to measure the vertical distance between an SMR 700Aplaced in nest 1400A and an SMR 700B placed in nest 1400B. In FIG. 19A,the SMR 700A is rotated within the nest 1400A so as to place its runoutreference line 1910 in the vertical direction toward the top of the SMR700A. The SMR 700B is rotated within the nest 1400B so as to place itsrunout reference line 1920 in the vertical direction toward the bottomof the SMR 700B. The true distance between the sphere center of SMR 700Aand the sphere center of SMR 700B is indicated by the line 1902. The SMRrunout error vector for SMR 700A is indicated by the vector 1904 and theSMR runout error vector for SMR 700B is indicated by the vector 1906.The resulting measurement of the length between the sphere centers isoff by an amount equal to the sum of the magnitudes of the vectors 1904and 1906. These errors appear in the measured length represented by thelength 1908.

In FIG. 19B, the SMR 700C is the same as the SMR 700A, but the SMR 700Ais rotated to place the runout reference line in the horizontalposition, which is the position at which it is perpendicular to the lineconnecting the centers of the SMRs in the nests 1400A and 1400B. The SMR700D is the same as the SMR 700B, but the SMR 700D is rotated to placethe runout reference line in the horizontal position. The true distancebetween the sphere center of SMR 700C and the sphere center of SMR 700Dis indicated by the line 1952. The SMR runout error vector for SMR 700Cis indicated by the vector 1954 and the SMR runout error vector for theSMR 700D is indicated by the vector 1956. The resulting length 1958 hasa length that is close to the true length 1952. The error resulting fromthe calculation of the length 1958 is known as a cosine error which isoften negligible, as shown in the example given for FIG. 16.

The error in the measurement of FIG. 19A could have been made smaller ifthe runout reference lines for 700A, 700B had both been aligned eitherup or down; however, the results in general are much better if therunout reference lines are rotated perpendicular to the line connectingthe sphere centers of the two SMRs. This is true not only for a verticaldirection but for any direction connecting two SMRs.

To simplify the alignment of the SMR runout, it is convenient for theoperator to know the direction of the maximum runout error vectorcomponent. This is easily accomplished if the reference point is alignedto the maximum runout error vector component, in other words, if the SMRrunout reference angle is set to zero. Alternatively, it could be set to180 degrees or another easily understood value such as +90 or −90degrees. This angle is a preferred and predetermined angle in the sensethat each SMR produced by a manufacturer has the reference point at thesame position relative to the maximum runout error vector.

The method of aligning a reference mark can also be applied to minimizeerrors in dimensional measurements in addition to the measurement oflength. An example of a dimensional measurement of a small displacementin the positions of the first SMR 1982, 1983 in the direction x′. Theorientation of the reference mark 932 shown in FIG. 19C is still correctfor this case. In other words, were the objective to sensitively measuresmall displacements of either the first nest or second nest along thedirection x′, the nest reference marks should be oriented as shown inFIG. 19C On the other hand, if the objective were to sensitively measuresmall displacement of either the first nest or second nest along thedirection z′, the optimum position for the reference mark 932 would bedifferent. In this case, the SMR runout error component should beperpendicular to the direction to be measured. As shown in FIG. 19D, theSMR reference ray 940 should be oriented perpendicular to the beamdirection but in the x′-y′ plane. There are two possible orientations inthis case, to the left of the beam as in 1987 or to the right of thebeam as 1988. The SMR reference may be oriented to minimize error in themeasurement of other dimensional quantities, as will be clear to one ofordinary skill in the art.

FIG. 20A shows a schematic representation 3000 of the azimuth axis 20and zenith axis 18 described in FIG. 1. Also shown are the azimuthmechanical axis (axle) 20 and the zenith mechanical axis (axle) 23corresponding to the azimuth axis 20 and zenith axis 18, respectively.The azimuth mechanical axis 24 rotates about the azimuth axis 20 by anangle 21. The azimuth axis 20 corresponds to a centerline 27 of theazimuth mechanical axis 24. The zenith mechanical axis 23 rotates aboutthe zenith axis by an angle 19. A perpendicular line 28 is drawn betweenthe azimuth axis and the zenith axis at the point of closest approach ofthe two axes. The perpendicular line 28 intersects the centerline 27 ina point 22. The length 29 of the perpendicular line between the azimuthaxis 20 and zenith axis 18 is the axis offset (AXOF) length 29. Becausein the mechanical arrangement of FIG. 1, the payload 15 rotates aboutthe zenith mechanical axis, while the zenith mechanical axis rotatesabout the azimuth mechanical axis, which is attached to the fixed base,it follows that there the intersection point 22 is stationary withrespect to the device frame of reference 30 of FIG. 1. For this reason,the point 22 may be considered to be the gimbal point of the device 10,that is to say the point about which the azimuth and zenith mechanicalaxes rotate. Notice, however, that the zenith axis 18 does not exactlyrotate about the gimbal point 22. However, mathematical compensationscan be made so that all rotations are referenced to the gimbal point.After making small compensations for beam offset and beam tilt, the beamof light 46 appears to emerge from a beam rotation point on the zenithaxis 18.

To summarize, it is mathematically convenient and customary in the artto select a gimbal point 22 as a stationary point within the device 10and to refer 3D coordinates measured by the device 10 back to thispoint. This means that mathematical compensations are made to accountfor non-ideal aspects of real-world mechanical axes. One such non-idealaspect is the axis offset 29. Another non-ideal aspect of the mechanicalaxes is axis non-squareness. In an ideal mechanical system, the azimuthand zenith axis are exactly perpendicular. In a real system, there issmall deviation from perpendicularity, which is an angular value calledthe axis non-squareness value. To get the measured 3D coordinates,mathematical methods are used to correct the distance and two anglesmeasured by the device 10 to refer these values to the gimbal point 22.

In a similar manner, in an ideal device 10, the beam of light 46 passesvirtually through the gimbal point 22. In a real system, the beam oflight is offset from the gimbal point 22 first by an axis offsetdistance 29. In addition, the beam of light 46 is offset from the beamrotation point (on the zenith axis 18). The offset is a small distancevalue in y″ and z″ in the y″-z″ plane of the payload frame of reference35 shown in FIG. 1.

In an ideal device 10, the beam of light 46 emerges from the device in adirection perpendicular to both the azimuth axis and the zenith axis. Ina real device 10, the beam of light 46 emerges slightly off this ideaangle. To move measured distance and two angles to coordinates with thetracker frame of reference, with the gimbal point as the origin,parameters may be used to mathematically account for these effects andreference all measurements to the origin. For example, in the type ofbeam steering mechanism described in device 10 of FIG. 1, the parametersTX, TY may account for beam offsets, and the parameters RX, RY mayaccount for the beam tilts (with respect to the ideal). It should beunderstood that other beam steering mechanisms, for example, mechanismsthat use mirrors, will have different methods of compensating for themechanical and optical imperfections in the system, but that the generalprinciples discussed herein are applicable to all such beam steeringmechanisms.

It is necessary to provide a reference distance for the distance meterwithin the device 10. Since the beam of light from the distance meterappears to emerge from the beam rotation point, it is necessary toprovide a way to refer any measured distances to this point. Methods fordoing this are discussed in detail hereinbelow.

The frontsight mode of the device 10 is its usual mode of operation. Thedevice illustrated in FIG. 20A is in the frontsight mode. In the figureshown, the zenith axis 18 is in front of the azimuth axis 20, but itcould equally well have been on the other side of (in back of) theazimuth axis. The term frontsight mode simply indicates that this is thenormal mode of operation of the device as defined by the devicemanufacturer.

Another mode of operation of the device is the backsight mode. To getinto the backsight mode, starting from the frontsight mode, the payloadis rotated about the azimuth axis by 180 degrees and rotated about thezenith axis to point the beam of light 46 back at the retroreflectortarget. As shown in FIG. 20B, an effect of putting the device 10 in tobacksight mode is to place the zenith mechanical axis on the oppositeside of the azimuth mechanical axis. In other words, if the axis offsetparameter is positive in the frontsight mode, it will be negative in thebacksight mode, and vice versa. For the case in which a vertex 820 of anSMR 700 is placed in line with the line of closest approach 28 as inFIGS. 20A and 20B, the backsight distance 47′ minus the frontsightdistance 47 is equal to twice the axis offset value.

FIG. 20C shows a schematic representation 3040 of the device 10 sendinga beam of light to an SMR 700 for the case in which the SMR is placed ina home measurement nest 17 of FIG. 1. The beam of light 46″ is emittedfrom the beam rotation point. In an embodiment, the distance meter isset to have a distance of zero at the point 18 in the frontsight mode.It reads a distance 3042 when the SMR 700 is placed in the home positionnest 17. The distance read by the device 10 with respect to the gimbalpoint 22 (following compensations), however, is a distance 48 from thegimbal point 22 to the vertex point 820.

To establish the beam rotation point as the zero point for the distancemeter, a separate procedure is carried out as is now described withreference to FIGS. 21A-C. In a first step illustrated in schematicrepresentation 3100 of FIG. 21A, a distance is measured between two SMRcenter positions. One way to measure this distance is to align a gimbalpoint 3112 of a laser tracker to a line that connects the centers of thetwo SMRs. The sphere center of the SMR 3120 when placed in the nest 3130may be referred to, for the purpose of this discussion, as the firstnest center. The sphere center of the SMR 3120′ when moved to the secondnest 3130′ may be referred to as the second nest center. A lineconnecting the first nest center and the second nest center may becalled the sphere center line. That portion of the sphere center linethat lies between the first sphere center and the second sphere centeris called the interior portion of the sphere center line, and thatportion of the sphere center line excluding the interior portion is theexterior portion.

The gimbal point 3112 of the device 3110 is placed at a point on theexterior portion. The distance 3124 of the beam of light 3114 from thegimbal point 3112 to the vertex point 3122 of the SMR in the first nestis measured. The SMR is moved to the second nest 3130′. The distance3126 of the beam of light 3116 from the gimbal point to the vertex point3122′ of the SMR in the second nest is measured. The distance 3126 minusthe distance 3124 is the distance between the vertex point 3122 and thevertex point 3122. However, for the geometry of FIG. 21A, the SMR deptherror is common mode and cancels out for the two length measurements.Hence the difference in the distances 3126 and 3124 is also the distancebetween the sphere centers of the SMRs 3120 and 3120′.

Two additional steps illustrated in FIGS. 21B, 21C may be carried out toset the distance 3042 to set the distance meter to have a distance ofzero at the beam rotation point (on the zenith axis 18). In a first stepillustrated in schematic representation 3140, the device in itsfrontsight mode is placed so that a gimbal point 3112′ of the device3110′ is on the interior portion. The distance meter measures thedistance 3142 from the gimbal point 3112′ to the vertex of the SMR 3120′and the distance 3144 from the gimbal point 3112′ to the vertex of theSMR 3120″. In a second step illustrated in the schematic representation3170 of FIG. 21C, the device 3110″ is placed in backsight mode. Themeasurements to the two SMRs are repeated to obtain distances 3172 and3174.

The distance 3126 should equal the sum of distances 3142 and 3144 if thedistance meter is correctly zeroed to the beam rotation point (on thezenith axis 18). To correct for any discrepancy from the ideal, anoffset distance is calculated using the formula offsetdistance=(distance 3126−(distance 3142+distance 3144))/2. The offsetdistance is added to each distance reading. Equivalently, we canconsider that the offset distance is set to zero the beam rotationpoint.

There are two different types of distance meters—absolute andincremental—that are reset somewhat differently. In the case of anincremental distance meter such as an interferometer, the distance isset to a known value at a given point. For example, it could be that alaser beam sent to an SMR sent to a home position nest is expected tohave a distance reading of 0.167 meters based on measurements made in afactory or laboratory. For an incremental distance meter, a beam oflight is sent to the SMR in the home position and set to read a value of0.167 meter. Afterwards, the device may count the number of wavelengthsshift in waves of light and multiply these by the wavelength of thelight in question (in the local air medium) to get the total change indistance. This change in distance is added to the original distance toget the distance at any later time.

In the case of an absolute distance meter (ADM), a beam of light mayagain be sent to a distance meter, but in this case the distance read bythe distance meter is compared to the known distance, which might againbe 0.167 meter. One or more parameters associated with the measurementof the ADM, such as a phase offset parameter, for example, are adjustedto give the expected reading of 0.167 meter. Thereafter the adjustedparameter(s) continues to be used in making corrections to the ADMreadings.

Although the way of resetting a distance meter is somewhat different inthe two cases—resetting to a distance for the incremental distance meterand resetting parameters for the ADM—in both cases, it is necessary tosend the beam of light from the device to the vertex of the SMR beforemaking the necessary compensations.

FIG. 21C is a schematic representation 3170 that illustrates a way todetermine the axis offset value 29. With the device in the backsightmode, the distance meter measures distances 3172 and 3174. The axisoffset value is calculated with the formula axis offset value=((distance3142+distance 3144)−(distance 3172+distance 3174))/4. The axis offsetvalue is used in transforming the measured distance and two angles intoa 3D coordinates in a coordinate system 30 centered on the gimbal point22.

The methods for setting the zero distance value for the distance meterin the device 10 discussed hereinabove have shown the distances measuredby the distance meter taken with respect to the SMR vertex points 820.However, each SMR has its own depth error, which means that the methodof FIG. 21 will give different results depending on the SMR or SMRsused. A way around this problem is to use SMR compensation parameters tomeasure to the SMR sphere center(s) rather than the sphere vertex. Forthe case shown in FIG. 21B, it is usually the case that the axis ofsymmetry of the SMRs 3120′ and 3120″ can be aligned to the beams oflight from the device 3110′. In this case, the effect of the runouterror is negligible. For example, suppose that the SMR runout error forthe SMR 3120″ is 12 micrometers, with the distance from the gimbal point3112′ equal to 2 meters. The error in the measured length is √{squareroot over (2²+(12·10⁻⁶)²)}−2 m=3.6·10⁻⁵ μm, which is a negligible value.As long as the axis of symmetry of the SMRs 3120′ and 3120″ can be wellaligned to the beams from the device 3110′, it is only necessary toincrease or decrease the measured distances 3142, 3144 to account forthe SMR depth error. By making this correction, the method describedabove with reference to FIGS. 21A-21C will be accurate regardless of theSMR depth error.

Some variations are possible in the procedures described in reference toFIGS. 21A-C. The method of FIG. 21 may be modified by obtaining areference artifact having a known distance between nests. The distancebetween spheres placed on the nests 3130 and 3130′ may be measured onceusing a Cartesian CMM or interferometer. If testing is done in aconstant temperature environment, say at 20° C., then the distancebetween the nests would not be expected to change, especially if theartifact is made of a material having a low coefficient of thermalexpansion (CTE). For example, the artifact may be made of carbon fibercomposite material having a low CTE, or it may be made of Invar orSuper-Invar.

In another case, different SMRs may be placed in the nests 3130 and3130′ rather than shifting one SMR between nests. Using two SMRs in thisway may save time in an automated procedure. In this case, the deptherror of each SMR is accounted for separately in determining setting thedistance meter to zero at the beam rotation point.

The discussion with regard to FIGS. 21A-C had to do with methods forsetting the distance meter to read correct values or for applyingcompensation or correction values to distance readings. An importantaspect of these corrections is to account for SMR depth error so thatdistance meter compensation is accurate regardless of the SMR deptherror. In the case of a device 10 that has a home position nest 17, theend result of the procedures of FIGS. 21A-C is a numerical value calledthe home reference distance, defined as the distance from the rotationpoint (on the zenith axis 18) to the center of an SMR (of givendiameter) placed in the home position nest.

For a device that does not have a home position nest, the end result ofthe procedures of FIGS. 21A-C is a correction to the distance meteritself. In other words, the processing of the distance meter is changedfollowing the procedure to make the sum of the distance readings 3142and 3144 equal the difference in the distance readings 3126 and 3124.Afterwards, this reset distance reading may be used to set a distance toa retroreflector fixed to the device. Such a fixed retroreflector may bemeasured whenever desired to remove drift from the distance meter

As stated in the preceding paragraph, for a device having a nest thatholds an SMR, the end result of the procedures of FIGS. 21A-C is a homereference distance, which is a numerical value. In an embodiment, thisnumerical value is made more accurate by correcting for SMR depth error.The home reference distance is saved within the memory of the device.

In routine use of the device 10, the home reference distance is used tocorrect the distance reading of an SMR placed at the home position nest17. Such routine correction may be useful in correcting drift in thedistance meter, which may occur over time and as a result of temperaturechanges and mechanical shocks. As explained in FIG. 20C and shown againin FIG. 22, a beam 46 may be sent to a vertex point 820 of an SMR 700 ina home position nest 17. If possible, the axis of symmetry of the SMR isaligned to the beam of light from the device. When this is possible, thedistance meter may be set a distance 3042 to the vertex 820 based on thehome reference distance and the SMR depth error without considering theSMR runout error vector component. For example, suppose that the SMR hasa sphere radius of 0.75 inch=19.05 mm, with its sphere vertex 820 adistance of 0.167 meter from the beam rotation point on the zenith axis18. Further suppose that the SMR runout error is 0.0005 inch=12.7micrometers. The SMR runout error produces an error in the measureddistance of √{square root over (0.167²+(12.7·10⁻⁶)²)}−0.167 m=4.83·10⁻¹⁰m, which is negligible.

In some cases, it is not possible to align the axis of symmetry of theSMR 700 with the beam direction 46. For example, in FIG. 22 the collar905 cannot be aligned to the axis of symmetry with having the collarcome into contact with the nest surface. Such contact is to be avoidedas it can cause the SMR to rise off the nest contact points, therebycausing an error.

In this case, it is advisable to account for the effects of the SMRrunout error vector component as well as the SMR depth error. This maybe done in two steps. In a first step, the SMR is placed in the nestwith the collar a certain distance off the nest surface. For example, aprescription might be to lower the collar until it touches the nestsurface and then raise the nest by 2 mm. Assuming that the operator canadjust the collar to within one millimeter of the desired value for anSMR having a radius of 19.05 mm, alignment is obtained to within about±3 degrees. In a second step, the SMR is aligned to place the referencepoint 932 at a specified orientation. For example, the prescriptionmight be to reference point 932 at the uppermost SMR position. Thecalculations discussed hereinabove with respect to FIGS. 9C, 9D and 12A,12D can then be carried out to correct the distance reading to accountfor the vector error. In other words, the home reference distance, whichis a value intended for the sphere center of an SMR in the home positionnest 17 is adjusted for the vector error to set the distance for the SMRvertex point, which is the actual point measured by the device 10. Analternative way to carry out the second step is to use the camera 56 ofFIG. 1 to determine the orientation of the SMR, as discussedhereinabove.

FIG. 23 shows electrical and computing components 2000 within andoutside the laser tracker 10, which is representative of a device usedto measure an SMR. These electrical and computing components are merelyrepresentative, and it should be understood that other configurationsare possible. A master processor 2070 sends and receives data messagesto processors within the laser tracker. These messages may be sent overa wired, optical, or wireless device bus 2030. Processing may beindependently carried out for functions within the laser tracker 10. Forexample, there may be a position detector processor 2012, azimuthencoder processor 2014, zenith encoder processor 2016, ADM processor2020, interferometer processor 2022, locator cameras processor 2024,indicator lights processor 2018, temperature electronics processor 2025,azimuth (AZ) and zenith (ZE) motor processor, and RFID and wirelessprocessor 2028. The RFID and wireless processor 2028 may be connected toan antenna 2029 for emitting or receiving radio frequency (RF) signals.The term processor as used herein is intended to include not onlycomputing devices, which might include microprocessors, FPGAs, and DSPs,but also electronic circuitry to perform functions needed to conditionthe signals to be sent to a computing device or memory. Such electroniccircuitry might include, for example, analog-to-digital converters ortemperature determination electronics. The master processor 2070 may beenclosed in a box such as the interface box 70 of FIG. 2. Alternatively,it may be integrated into the electronics internal to the tracker body.The signals from the master processor may go to an external computer 25or be connected to a network 2044, 2042.

An electrical memory component within 2000 may be used to storeinformation. Such information may be used by the processor or may betransmitted to a remote processor by wired or wireless means. Theinformation may include a serial number and SMR parameters as discussedhereinabove.

While the description above refers to particular embodiments of thepresent invention, it will be understood that many modifications may bemade without departing from the spirit thereof. The accompanying claimsare intended to cover such modifications as would fall within the truescope and spirit of the present invention.

The presently disclosed embodiments are therefore to be considered inall respects as illustrative and not restrictive, the scope of theinvention being indicated by the appended claims, rather than theforegoing description, and all changes which come within the meaning andrange of equivalency of the claims are therefore intended to be embracedtherein.

What is claimed is:
 1. A method of measuring a spherically mountedretroreflector (SMR) with a device, the method comprising the steps of:providing a first SMR, the first SMR including a first body and a firstretroreflector, the first SMR including a first reference point, thefirst body having a first spherical exterior portion that has a firstsphere center and a first sphere radius, the first body containing afirst cavity, the first cavity sized to hold the first retroreflector,the first cavity open to a region outside the first body, the firstretroreflector at least partially disposed in the first cavity, thefirst retroreflector being an open-air cube-corner retroreflector, thefirst retroreflector having a first set of three mutually perpendicularplanar reflectors that intersect in a first set of three lines and in acommon first vertex point, the first cavity including an air-filledregion interior to reflecting surfaces of the first set of three planarreflectors, the first retroreflector having a first axis of symmetryrelative to the first set of three lines, the first SMR having a firstSMR runout plane perpendicular to the first axis of symmetry and passingthrough the first sphere center, the first SMR having a first SMRintersection point, the first SMR intersection point being a point ofintersection of the first axis of symmetry with the first SMR runoutplane, the first SMR having a first error vector extending from thefirst vertex point to the first sphere center, the first SMR errorvector having a first SMR depth error vector component and a first SMRrunout error vector component, the first SMR depth error vectorcomponent being a vector that extends from the first vertex point to thefirst SMR intersection point, the first SMR runout error vectorcomponent being a vector that extends from the first SMR intersectionpoint to the first sphere center, the first SMR depth error vectorcomponent having a magnitude equal to a first SMR depth error; providingthe device, wherein the device has a device frame of reference fixedwith respect to a base of the device and a light source that emits afirst beam of light, the device being configured to measure a targetdistance and two target angles from the device to the first vertexpoint, the two target angles given with respect to the base; providing aprocessor and a memory; providing computer readable media havingcomputer readable instructions which when executed by the processorcalculates first three-dimensional (3D) coordinates of the first spherecenter in the device frame of reference; determining the first SMR deptherror and the first SMR runout error vector component; storing as firststored values the first SMR depth error and a numerical representationof the first SMR runout error vector component; reading by the processorthe first stored values; and performing a first measurement, the firstmeasurement including steps A through J: A) providing a rule fororienting the first SMR to obtain a first preferred orientation of thefirst SMR; B) determining, by the operator, the first preferredorientation of the first SMR based at least in part on the rule; C)orienting, by the operator, the first SMR in the first preferredorientation, the first preferred orientation based at least in part onthe first reference point and on the axis of symmetry; D) determining bythe processor the first preferred orientation in the device frame ofreference based at least in part on the rule; E) sending the first beamof light from the light source to the first vertex point in a first beamdirection and in response receiving at the device a first reflectedlight; F) measuring, from the device to the first vertex point, a firsttarget distance and a first set of the two target angles based at leastin part on the first reflected light, the first target distance furtherbased at least in part on a speed of light over a path traveled by thefirst beam of light; G) determining the first beam direction in thedevice frame of reference based at least in part on the first set of thetwo target angles; H) determining with the processor 3D coordinates ofthe first vertex point in the device frame of reference based at leastin part on the first target distance and the first set of the two targetangles; I) executing by the processor the computer readableinstructions, the computer readable instructions performing amathematical transformation of the 3D coordinates of the first vertexpoint to obtain the 3D coordinates of the first sphere center in thedevice frame of reference, the mathematical transformation includingtranslating the 3D coordinates of the first vertex point along the firstbeam direction by the first SMR depth error and along a directionperpendicular to the first beam direction, the translating along thedirection perpendicular to the first beam direction being based at leastin part on the first beam direction, the numerical representation of thefirst SMR runout error vector component, and the first preferredorientation of the first SMR; and J) storing the 3D coordinates of thefirst sphere center.
 2. The method of claim 1 wherein, in the step ofproviding a processor and a memory, the processor is included in thedevice.
 3. The method of claim 1 wherein, in the step of providing aprocessor and a memory, the processor is included in a computinginstrument external to the device.
 4. The method of claim 1 wherein: inthe step of providing a first SMR, the first SMR has a first SMRreference plane that includes the first reference point and the firstaxis of symmetry, there being a first SMR reference ray coincident witha line of intersection between the first SMR reference plane and thefirst SMR runout plane, the first SMR reference ray beginning at thefirst SMR intersection point and lying in a half of the first SMRreference plane that includes the first reference point, the first SMRrunout error vector component having a first SMR runout reference angle,the first SMR runout reference angle being an angle between the firstSMR reference ray and the first SMR runout error vector component, alength of the first SMR runout error vector component being equal to afirst SMR runout error; and in the step of storing as first storedvalues the first SMR depth error and a numerical representation of thefirst SMR runout error vector component, the numerical representation ofthe first SMR runout error vector component includes the first SMRrunout error and the first SMR runout reference angle.
 5. The method ofclaim 4 wherein, in the step of executing by the processor the computerreadable instructions, the translating along a direction perpendicularto the first beam direction includes translating in a planeperpendicular to the first beam direction by an amount equal to thefirst SMR runout error in a direction given by a first beam runoutreference angle relative to a first beam reference ray, the first beamreference ray coinciding with a line of intersection between a firstbeam reference plane and a first beam runout plane, the first beamreference ray beginning at a first beam intersection point and lying ina half of the first beam reference plane that includes the firstreference point, the first beam reference plane being a plane thatincludes the first reference point and the first beam direction, thefirst beam runout plane being a plane perpendicular to the first beamdirection and that includes a first beam intersection point, the firstbeam intersection point being a point translated from the first vertexpoint along the first beam direction by the first SMR depth error, thefirst beam runout plane being a plane perpendicular to the first beamdirection and passing through the first beam intersection point.
 6. Themethod of claim 1 wherein, in the step of providing a first SMR, thefirst SMR is provided with a first collar, the first collar configuredto be gripped by an operator.
 7. The method of claim 6 wherein, in thestep of providing a first SMR, the first reference point is included onthe first collar.
 8. The method of claim 7 wherein, in the step ofproviding a first SMR, the first reference point is located on one ofthe group consisting of a reference mark, a serial number, aone-dimensional barcode, a two-dimensional barcode, a radio frequencyidentification tag, and a reflective region.
 9. The method of claim 1wherein, in the step of performing a first measurement, the firstmeasurement includes aligning by the operator the axis of symmetry tothe first beam direction.
 10. The method of claim 9 wherein, in the stepof providing a rule for orienting the first SMR to obtain a firstpreferred orientation of the first SMR, the rule is to rotate the SMRabout the first axis of symmetry until the first SMR reference plane isaligned to a plane that includes a gravity vector and the first beam oflight.
 11. The method of claim 9 wherein, in the step of providing arule for orienting the first SMR to obtain a first preferred orientationof the first SMR, the rule is to rotate the SMR about the first axis ofsymmetry until the first SMR reference plane is aligned to a plane thatincludes an axis of rotation of the device and the first beam of light.12. The method of claim 11 wherein, in the step of providing a rule fororienting the first SMR to obtain a first preferred orientation of thefirst SMR, the axis of rotation is an azimuth axis.
 13. The method ofclaim 11 wherein, in the step of providing a rule for orienting thefirst SMR to obtain a first preferred orientation of the first SMR, theaxis of rotation is a zenith axis.
 14. The method of claim 9 wherein, inthe step of providing a rule for orienting the first SMR to obtain afirst preferred orientation of the first SMR, the rule is further basedon a first dimensional quantity of interest, wherein the firstdimensional quantity of interest is given with respect to a firstmeasurement line.
 15. The method of claim 14 wherein, in the step ofproviding a rule for orienting the first SMR to obtain a first preferredorientation of the first SMR, the first dimensional quantity of interestis a first length between two points on the first measurement line, andthe rule is to rotate the SMR about the first axis of symmetry until thefirst SMR reference ray is perpendicular to the first measurement line.16. The method of claim 1 wherein, in the step of providing a first SMR,the first SMR further includes an information storage element.
 17. Themethod of claim 16 further including a step of storing on theinformation storage element the first stored values.
 18. The method ofclaim 17 wherein, in the step of providing a first SMR, the first SMR isprovided with a first collar, the first collar configured to be grippedby an operator, the information storage element being affixed to orintegrated into the collar.
 19. The method of claim 16 wherein theinformation storage element is selected from the group consisting of aone-dimensional barcode, a two-dimensional barcode, and a radiofrequency identification tag.
 20. The method of claim 19 wherein, in thestep of providing the device, the device further includes a storageelement reader, the storage element reader configured to read theinformation stored in the information storage element.
 21. The method ofclaim 17 wherein, in the step of storing on the information storageelement, the information storage element is a one-dimensional or atwo-dimensional barcode, and wherein, in the step of providing a device,the device further includes a camera configured to read the informationstorage element when the first SMR is placed in a kinematic supportaffixed to the device.
 22. The method of claim 17 wherein the step ofstoring on the information storage element the first stored valuesfurther includes a step of storing an SMR serial number.
 23. The methodof claim 9 wherein, in the step of performing a plurality of firstmeasurements, the operator uses an alignment tool to assist in thealigning.
 24. The method of claim 23 wherein, in the step of performinga plurality of first measurements, the alignment tool includes an opaquecover that fits over the first collar, the cover including a visiblemark, the visible mark being a circle or a crosshair.
 25. The method ofclaim 23 wherein, in the step of performing a plurality of firstmeasurements, the alignment tool includes a mirror that fits over thefirst collar.
 26. The method of claim 24 wherein, in the step ofperforming a plurality of first measurements, the mirror includes avisible mark, the visible mark being a circle or a crosshair.
 27. Themethod of claim 22 wherein, in the step of performing a plurality offirst measurements, each of the first measurements include steps ofsending the first beam of light from the device in a circular patternand aligning by the operator the axis of symmetry to center the SMR onthe circular pattern.
 28. The method of claim 23 wherein, in the step ofperforming a plurality of first measurements, the alignment tool isselected from the group consisting of a reflective strip, a finger, awindow onto which a circle or crosshair has been marked.
 29. The methodof claim 1 wherein: the step of providing a first SMR further includesproviding a first temperature sensor, the first temperature sensoraffixed to the first SMR; the step of performing a plurality of firstmeasurements further includes measuring a first temperature of the firsttemperature sensor; and in the step of executing by the processor thecomputer readable instructions, the 3D coordinates of the first spherecenter are further based the first temperature measured by the firsttemperature sensor.
 30. The method of claim 1 wherein, in the step ofmeasuring, from the device to the first vertex point, a first targetdistance and a first set of the two target angles, the first SMR is heldin contact with a first surface at a first contact point.
 31. The methodof claim 30 wherein the step of a making a first measurement is repeatedmultiple times to obtain a plurality of first measurements, theplurality of first measurements resulting in a plurality of firstcontact points and a corresponding plurality of first sphere centers,the plurality of first sphere centers having a corresponding pluralityof 3D coordinates of the first sphere centers.
 32. The method of claim31 further including a step of selecting a first chosen contact pointfrom among the plurality of contact points, there being a correspondencebetween the first chosen contact point and a first chosen sphere centerpoint, the method including: selecting a first subset of the pluralityof first contact points; selecting a second subset of the stored 3Dcoordinates of the first sphere center, each element of the secondsubset corresponding to an element of the first subset; determining afirst surface normal vector based at least in part on the second subset;and determining the 3D coordinates of the first chosen contact pointbased at least in part on the 3D coordinates of the first chosen spherecenter point, the first surface normal vector, and a first radius, thefirst radius being a value of the first sphere radius.
 33. The method ofclaim 32 further including steps of: measuring a first radius; storing afirst radius parameter, the radius parameter being the first radius or afirst radius delta, the first radius delta being the first radius minusa reference value of the first radius; and reading by the processor thefirst radius parameter.
 34. The method of claim 15 further includingstoring on the information storage element the first radius parameter.